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January 15, 2000
O P - S F N E T Volume 7, Number 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Editor:
Martin Muldoon muldoon@yorku.ca
The Electronic News Net of the SIAM Activity Group
on Orthogonal Polynomials and Special Functions
Please send contributions to: poly@siam.org
Subscribe by mailing to: poly-request@siam.org
or to: listproc@nist.gov
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Today's Topics
1. From the Editor
2. Research Perspectives
3. NATO ASI and Conference: "Special Functions 2000"
4. Conference on Reproducing Kernel Hilbert Spaces
5. Krawtchouk Conference
6. Session on Adaptive Quadrature and Cubature Formulae
7. Dalian Symposium on Analysis, Combinatorics and Computing
8. Reports on OPSFA-Patras
9. Report on AMADE Conference in Minsk
10. Report on Benin Workshop
11. Askey issues of Methods and Applications of Analysis
12. Changes at Methods and Applications of Analysis
13. Review Of "Special Functions" by Andrews, Askey and Roy
14. Doron Zeilberger's Maple Packages and Programs
15. Question on Schrodinger equations
16. SIAM Student Paper Prizes
17. OP-SF preprints in xxx archive
18. Changes of Address, WWW Pages, etc
19. Subscribing to OP-SF NET
20. Obtaining back issues of OP-SF NET and submitting contributions
to OP-SF NET and Newsletter
Calendar of Events:
2000
March 27-31: Workshop on Quantum Groups, Morelia, Mexico 6.5 #3
April 14-18: Workshop on Orthogonal Polynomials, Approximation and
Harmonic Analysis, Inzell, Germany 6.6 #2
April 16-21: Conference on Reproducing Kernel Hilbert Spaces,
Krakow, Poland 7.1 #4
May 11-13: VIII International Krawtchouk Conference, Kiev, Ukraine 7.1 #5
May 17-20: Symposium on Trends in Approximation Theory,
Nashville, Tennessee, USA 6.5 #4
May 29 - June 9: Special Functions 2000: Current Perspective
and Future Directions, Tempe, Arizona, USA 6.5 #2, 7.1 #3
July 3-7: Alhambra 2000, a Joint Mathematical European-Arabic
Conference 6.4 #7
July 10-14: SIAM Annual Meeting in Puerto Rico
See: http://www.siam.org/meetings/an00/index.htm
July 17-22: I Colloquium on Lie Theory and Applications,
Vigo, Spain 6.4 #8
July 19-26: Third World Congress of Nonlinear Analysts,
Catania, Italy (including session on
"Adaptive quadrature and cubature formulae". 7.1 #6
July 24-28: Summer School "Orthogonal Polynomials and Special
Functions", Laredo, Spain. 6.6 #3
August 5-8: International Symposium on Analysis, Combinatorics
and Computing, Dalian, China 7.1 #7
August 14-18: International Symposium on Applied Mathematics,
Dalian, China 6.5 #5
Topic #1 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: From the Editor
The year 2000 promises to be a busy one with respect to conferences and
workshops in our area. The NATO ASI and conference in Tempe, Arizona, USA
form May 29 to June 9 promises to be a major event but here are several
other workshops and conference in various parts of the world with at least
tangential interest for members of our Activity Group. Don't forget to
submit information on any relevant events which are not listed here.
Included here are reports on some 1999 events. I especially enjoyed Bill
Connett's report from OPSFA-Patras.
Topic #2 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Walter Van Assche
Subject: Research Perspectives
As a follow-up of the Honk Kong panel discussion, the SIAM activity group
will maintain a list of "research perspectives" on the web. The activity
group homepage will soon contain a link to a list of possible directions
in research relevant for (young) people interested in our field. This link
will be coordinated by Walter Van Assche. Please send possible suggestions
and items for inclusions to walter@wis.kuleuven.ac.be .
Topic #3 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Sergei Suslov
Subject: NATO Advanced Study Institute and International Conference:
"Special Functions 2000"
[This is an updated version of the announcement in OP-SF NET 6.5, Topic
#2. We emphasize the early deadline February 21, 2000 for application for
financial support. The application form is at the website:
http://math.la.asu.edu/~sf2000/index.html
The reason for the deadline is that the organizers have to submit a list
of participants to NATO at an early date in order to get funding.
Applications are especially welcome from graduate students and young
researchers.]
NATO Advanced Study Institute:
"Special Functions 2000"
Arizona State University
Tempe, Arizona, USA
May 29 to June 9, 2000
Objective of the ASI:
to summarize results in special functions and their diverse applications
obtained over the last three decades and to discuss future directions.
Topics:
Orthogonal polynomials and special functions in one and several variables,
asymptotics, continued fractions, applications to number theory,
combinatorics and mathematical physics, integrable systems, harmonic
analysis and quantum groups, Painleve classification, and others.
Lecturers:
G. Andrews, Pennsylvania State University, USA
R. Askey, University of Wisconsin, Madison, USA
P. Deift, Courant Institute, USA
C. Dunkl, University of Virginia, USA
A. Grunbaum, University of California, Berkeley, USA
M.E.H. Ismail, University of South Florida, Tampa, USA
A. Its, Indiana University - Purdue University, Indianapolis, USA
E. Koelink, Technische Universiteit Delft, The Netherlands
T. Koornwinder, KdV Institute, University of Amsterdam, The Netherlands
I. Macdonald, Queen Mary College, London, England (not confirmed)
S. Milne, The Ohio State University, USA
O. Njastad, Norwegian University of Science & Technology, Norway
M. Rahman, Carleton University, Ottawa, Canada
V. Spiridonov, Joint Institute of Nuclear Research, Dubna, Russia
D. Stanton, University of Minnesota, USA
S. K. Suslov, Arizona State University, USA
N. Temme, CWI, Amsterdam, The Netherlands
V. N. Tolstoi, Moscow State University, Russia
L. Vinet, McGill University, Montreal, Canada
A. Zhedanov, Donetsk Institute for Physics and Technology, Ukraine
International Organizing Committee:
Sergei Suslov, Arizona State University, USA
(Director from NATO country)
Vyacheslav Spiridonov, Joint Institute for Nuclear Research,
Dubna, Russia (Director from Partner country)
Tom Koornwinder, KdV Institute, University of Amsterdam, The Netherlands
Luc Vinet, McGill University, Montreal, Canada
Local Organizing Committee:
Joaquin Bustoz, Arizona State University (Chair)
Mourad Ismail, University of South Florida
Sergei Suslov, Arizona State University
Sponsors:
NATO Scientific and Environmental Affairs Division,
Arizona State University, Wolfram Research, and
Centre de Recherches Mathematiques, Universite de Montreal
Address:
Advanced Study Institute SF2000
Arizona State University
Department of Mathematics
Box 871804
Tempe, AZ 85287-1804
U.S.A.
E-mail: sf2000@math.la.asu.edu
Fax: 1-480-965-8119
Webpage: http://math.la.asu.edu/~sf2000/index.html
Application form is available on the webpage. Young researchers and
graduate students from NATO and Partner Countries are especially
encouraged to apply. Applications for financial support must be received
no later then February 21, 2000. Decision will be made by February 28,
2000.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
International conference:
"Special Functions 2000: Current Perspective and Future Directions"
May 29 to June 9, 2000
Arizona State University
Tempe, Arizona, USA
This conference will run concurrently with a NATO ASI and will be
supported by the National Science Foundation and Arizona State University.
Young researchers and graduate students from the US, Latin American
countries and Eastern European countries are encouraged to apply for
contributed presentations and/or financial support to the address:
Special Functions 2000
Arizona State University
Department of Mathematics
Box 871804
Tempe, AZ 85287-1804
U.S.A.
E-mail: sf2000@math.la.asu.edu
Fax: 1-480-965-8119
Web page: http://math.la.asu.edu/~sf2000/index.html
Application form is available on the webpage.
Application deadline is February 21, 2000.
Decision will be made by February 28, 2000.
Topic #4 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Franek Szafraniec
Subject: Conference on Reproducing Kernel Hilbert Spaces
The long maturing idea of organizing a conference in Krakow to commemorate
the 90th anniversary of introducing the reproducing kernel property by
Stanislaw Zaremba has become a reality. Now I can announce the conference
is going to be in April 2000, from the 16th till the 21st . The aim is to
gather people who work in areas to which RKHS pertains like function
theory, differential equations, operator theory or probability, so to
mention some of them (even so abstract domain as operator algebras is not
free of it: the famous GNS construction can be viewed as an application of
this property).
The first announcement will appear towards the end of January 2000 and
will be distributed by email. You can express your interest by sending an
email to rkhs2000@im.uj.edu.pl
Franek Szafraniec
E-mail: fhszafra@im.uj.edu.pl,
[also umszafra@cyf-kr.edu.pl or fhszafra@impan.gov.pl].
Topic #5 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Charles Dunkl
Subject: Krawtchouk Conference
The VIII International Conference devoted to the memory of Academician M.
Krawtchouk (or Kravchuk) (1892-1942) will be held May 11-13, 2000, in
Kyiv (Kiev), Ukraine. It is sponsored by the National Technical University
of Ukraine (KPI), the Institute of Mathematics of the Ukrainian National
Academy of Sciences, the National Taras Shevchenko University, and the
National Dragomanov Pedagogical University.
Programme sections:
(1) differential and integral equations, their applications
(2) algebra, geometry, mathematical and numerical analysis
(3) history of probability and mathematical statistics,
(4) history, methods of teaching of mathematics
Contact person:
Prof. Nina Virchenko (KPI)
Tel: +380 44 441 14 41
e-mail: syta@imath.kyiv.ua random@imath.kyiv.ua
(there is a $50 registration fee for foreign attendees), abstract deadline
is 1 March 2000.
Conference Web page:
http://www.isir.minsk.by/~zelenkov/physmath/kr_polyn/conf8.html
Topic #6 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Sever Dragomir
Subject: Organising a Session "Adaptive quadrature and cubature formulae"
I have been appointed to organize a session within the "Third Congress of
Nonlinear Analysts" which will be held during July 19-26, 2000 in
Catania, Sicily, Italy, on the topic "Adaptive quadrature and cubature
formulae".
In addition to the classical approach for adaptive quadrature and cubature
formulae which will be welcome in that section, we would like to encourage
the following topics in Theory of Inequalities which are related to
Numerical Integration:
- Ostrowski Type Inequalities
- Hermite -Hadamard Type Inequalities
- Gruss type inequalities
- Trapezoid, Midpoint, Lobatto, Newton-Cotes Type (Rules and)
Inequalities
- Integral Inequalities of Iyengar, Mahajani, Fink, etc... type where the
integrals are estimated in terms of Polynomials, Series etc...
- Any other integral inequality which might be of help in approximating
Riemann, Riemann-Stieltjes, Lebesgue or other integrals (Bochner,
Denjoy, Perron, Henstock etc...)
If you are interested to participate, please let me know before the 20th
of December and I will be able to post you the corresponding documents
to register.
For information on The Third World Congress of Nonlinear Analysts
(WCNA-2000) please consult the web site:
http://www.fit.edu/AcadRes/math/wcna/wcna2000.htm
Sever S. Dragomir
Topic #7 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Li Zhongkai
Subject: International Symposium on Analysis, Combinatorics and Computing
First Announcement: International Symposium on Analysis, Combinatorics
and Computing, Dalian, P. R. China, August 5-8, 2000
Objective
The purpose of this conference is to provide a forum for an exchange
of ideas among experts in the various topics listed below, and to
disseminate information on recent advances made in these areas.
Session Topics
1. Special Functions and its Applications
2. Combinatorics and its Applications
3. Approximation Theory and Numerical Analysis
4. Harmonic and Wavelet Analysis
Sponsored by
Dalian University of Technology
Organizing Committee
Chairman: Leetsch C. Hsu (Xu, Lizhi) (Dalian, PRC)
Members: Tian-Xiao He (Illinois, USA)
Zhongkai Li (Beijing, PRC)
Jun Wang (Dalian, PRC)
Sining Zheng (Dalian, PRC)
Academic Committee
Richard Askey (Madison, USA)
Paul L. Butzer (Aachen, Germany)
Guochen Feng (Changchun, PRC)
Leetsch C. Hsu (Dalian, PRC)
Peter Shiue (Las Vegas, USA)
Lewis Solomon (Madison, USA)
Zhexian Wan (Beijing, PRC)
Renhong Wang (Dalian, PRC)
Registration fee (including the official fee for the conference and the
fee for a reception banquet, daily breakfast, lunch and dinner, but not
the room fee. Each participant should pay his room fee separately.)
US$250 before May 31, 2000
US$300 after May 31, 2000
Call for Talks and Registration
The organizing committee encourages early registration and
submission of original technical and unpublished papers
related to the above session topics. Those who reply to
the organizers by e-mail or post-mail before February 15,
2000, will receive directly the second announcement,
in which the official forms for registration and
accommodation are included. Replies after this date will
also be accepted. Abstracts of contributed talks must
be received by June 30, 2000.
Invited Speakers:
Richard Askey (USA)
Paul L. Butzer (Germany)
Mourad Ismail (USA)
Peter Shiue (USA)
Lewis Solomon (USA)
Please contact one of the members of the organizing committee
if you are interested in this symposium or have any questions:
Jun Wang
Department of Applied Mathematics
Dalian University of Technology
Dalian 116024, P. R. CHINA
Email: junwang@dlut.edu.cn
Fax: 86-411-4708360
Sining Zheng
Department of Applied Mathematics
Dalian University of Technology
Dalian 116024, P. R. CHINA
Email:snzheng@dlut.edu.cn
Fax: 86-411-4708360
Zhongkai Li
Department of Mathematics
Capital Normal University
Beijing 100037, P. R. CHINA
Email: lizk@mail.cnu.edu.cn
Tel. 86-10-68462115
Tian-Xiao He
Department of Mathematics
Illinois Wesleyan University
Illinois, USA
Email: the@sun.iwu.edu
Tel: 309-556-3089
Remarks:
1. This conference will be held at the Dalian University of Technology,
Dalian, China, from August 5 to 8, 2000. For information about the
University and the City of Dalian, please visit the following web
sites:
http://www.dlut.edu.cn
http://www.china-dalian.com/100
2. If you are interested in or wish to participate in the conference,
please let us know your following information as soon as possible,
which are necessary for you to go through your Chinese visa:
(1) Full name (First) (Last)
(2) Citizenship
(3) Date of birth (month, day, and year)
(4) City and country of birth
(5) Passport number
(6) Correspondence address
Topic #8 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Reports on OPSFA-Patras
The Fifth International Symposium on Orthogonal Polynomials, Special
Functions and their Applications (OPSFA, for short), was held in Patras,
Greece, September 20 - 24, 1999. This was a conference in a European
series including Bar-Le-Duc (1984), Segovia (1986), Erice (1990), Granada
(1991, VII SPOA), Evian (1992), Delft (1994, Stieltjes centenary) and
Seville (1997, VIII SPOA); it certainly lived up to reputation of that
series for the excellence of the program and organization.
The Symposium was dedicated to Professor Ted Chihara in honour of his many
contributions to the subject of Orthogonal Polynomials. In fact the
opening ceremony consisted of a presentation to Chihara, a talk on his
work by Walter Van Assche and a characteristically modest lecture by Ted
entitled "Orthogonal Polynomials - a view from the wings". There was a
very full programme of plenary and contributed talks.
The main events were held in a new building at the magnificently located
University of Patras, the participants being bussed from nearby hotels to
the sessions and to the extensive program of social events. Though
Thursday was announced as a "Greek evening" (with respect to food and
entertainment) but it was quickly observed by the participants that every
evening could be so characterized. The local organizers themselves set a
great example for singing and dancing and succeeded in drawing all
participants.
The proceedings of the Symposium will appear as a special volume of the
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. The proceedings volume
is expected to include a report on a session for open problems which
concluded the symposium.
The next meeting in the European series on Orthogonal Polynomials will be
held in Italy in 2001, possibly in late June though the location and
exact dates have not been determined. The contact person is Andrea
Laforgia (laforgia@dma.uniroma3.it).
Here are reports from two other participants: Marcel de Bruin and Bill
Connett.
Report from Marcel de Bruin
September 20--24, 1999, the city of Patra (Greece, approximately 200
kilometers West from Athens), hosted the "Fifth International Symposium on
Orthogonal Polynomials, Special Functions and their Applications".
The local organizing committee consisting of Evangelos Ifantis, Chrysoula
Kokologiannaki and Panayiotis Siafarikas succeeded, with the aid of
Eugenia N. Petropoulou and Kiriaki Vlachou to set a standard of both
scientific and social level that will be difficult to better.
On one hand the scientific program with plenary lectures in the morning,
followed by research seminars in parallel sessions and the social program
on the other hand showed unexpected talents of many a participant.
Central was the guided visit to the ancient city of Olympia: history
looked over our shoulders to see how the mathematicians of today shape the
history of tomorrow. And each day the recurrent happening of the evening
meal that should be called a `social gathering'.
There it became clear that not only mathematics linked the participants
together, but also the intricacies of the `links and braids' of the steps
of the Greek dance. Greek music united many and succeeded in loosening up
a community that is usually considered `stuffy' by the outside world.
Other documents will give an account of the main mathematical
achievements. I can only say that this was a superbly organised conference
and conclude this with a well meant
$E\upsilon\chi\alpha\rho\iota\sigma\tau\omega\ \pi o\lambda\upsilon$
From: William Connett
The Fifth International Symposium on Orthogonal Polynomials, Special
Functions and their Applications which took place in Patras Greece from
September 20 to 24, 1999, is the most recent of a series of primarily
european conferences focused on these questions. It is inspiring to see
how the fields of orthogonal polynomials and special functions have grown
since the first of these series of meetings in Bar-Le-Duc in 1984. Over
160 people appeared in the provincial University of Patras in the middle
of the semester to participate in one of the most intense scientific
meetings I have ever attended. With representatives from thirty-two
countries in attendance, it was truly one of the most cosmopolitan
meetings, it has ever been my pleasure to attend. A field of mathematics
that once was the special interest of a few specialists in Northern
Europe, is now flourishing in Spain, Italy, Portugal, and Greece. It was
also heartening to see that the large number of mathematicians from the
Maghreb in attendance. If Ferdinand Braudel was writing his great book "La
Mediterranee et la Monde Mediteraneen..." today, he would have to a
chapter on the study of orthogonal polynomials as one of the great
unifying trans-cultural themes of the Mediterranean basin.
There were talks from 9:00 am to 1:30 pm, a two hour break for lunch,
and then more talks from 3:30 to 7:00 pm every day. After the talks, the
very energetic organizers took us off to visit some great ruin, and then
about the time I was longing for bed, we would begin dinner around 10:00
pm. After dinner the bouzouki music began and there was general dancing
led by our Greek colleagues who are stronger human beings than I. We would
go to bed at 1:00 am, and then start over the next day. By the fourth day
of the conference there were middle aged mathematicians asleep leaning
against trees all over the lovely campus. The most impressive single event
in the social program was our visit to Olympus, where Walter van Assche
was challenged to a foot race in the Olympic stadium by his student Els
Coussement. Age triumphed over beauty! Walter was rewarded for his
olympian efforts with the presentation of the traditional wreath of
laurels on the last day of the conference.
The conference was honoring the work of Ted Chihara, and the opening
session of the conference was presented by Walter van Assche who gave an
overview of Chihara's many accomplishments. Then Professor Chihara
responded with his typical modesty, and gave a very personal, and
delightful interpretation of the developments in orthogonal polynomials
over the last half century. There were eight other plenary lectures, and
over one hundred research seminars, so it will be impossible to give
anything but a very personal, selective, and impressionistic description
of the many fine papers. The plenary lecture that I was most interested in
was Lance Littlejohn's presentation of his and Norrie Everitt's progress
on the "Erice Conjecture". These results are part of the effort to develop
a complete theory of multivariate orthogonal polynomials that are the
eigenfunctions of differential operators. Walter Gautschi gave a
magisterial overview of the problems that occur when polynomials are used
for quadrature when there is a pole near the interval of integration. The
lecture of Arno Kuijlaars was a personal revelation, since I knew very
little about the asymptotics of polynomials orthogonal with respect to
Freud weights, and Kuijlaars' elegant presentation brought this corner
alive to me.
I must be even more selective in discussing the research seminars.
Nico Temme continued his efforts to fill in my vast ignorance about
asymptotics with a very clear talk about obtaining the asymptotics for
polynomials in the Askey scheme as limits of the asymptotics of other
polynomials in that scheme that we already understand. Kathy Driver gave a
provocative and delightful report on what the zeros of the ultraspherical
polynomials do when the parameter is less than minus one half. Wojciech
Mlotkowski reported on some joint work with Ryszard Szwarc. They have
found a new and very clever way to prove the non-negativity of the
linearization coefficients for polynomials supported on discrete measures.
And finally, the last talk on the last day of the conference, when the
participants were near mental and physical exhaustion, the members of the
organizing committee (Ifantis, Kokologiannaki, and Siafarikas) presented a
very nice sufficient condition for the support of the orthogonality
measure of a family of polynomials to be the entire interval. I was tired.
They must have been near collapse. What a display of "paidea".
I came to Greece not knowing what to expect. I was awed by the
science, the land, and the people. To paraphrase Alan Bates's line at the
end of that famous movie, "Panos, Chrysoula, Teach me to dance!"
Topic #9 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Sergei Rogosin
Subject: Report on AMADE Conference in Minsk
The international conference "Analytic Methods of Analysis and
Differential Equations" (AMADE) took place September 14-18, 1999 in
Minsk, Belarus. It was organized by the Belarusian State University, the
Belarusian National Academy of Sciences together with Moscow State
University and the Computer Center of the Russian Academy of Sciences. It
was held at the Olympic Sport Center "Staiki" which is situated 10 km from
Minsk, the capital of Belarus.
More than 320 mathematicians confirmed their interest in the Conference.
Abstracts of their reports were published in "Abstracts of AMADE". 165
scientists from Algeria, Australia, Belarus, France, Germany, Great
Britain, Italy, Japan, Korea, Lithuania, Poland, Portugal, Russia, Spain,
Ukraine and USA took part in AMADE.
There were 18 plenary invited lectures and 93 sectional talks on various
modern problems of integral transforms, special functions, differential
equations, operator theory, approximation and fractional calculus.
Plenary invited lectures were given by the following mathematicians:
Burenkov, V.I. (Great Britain): Extension theorems for spaces of
differentiable functions defined on strongly degenerated domains.
Gaishun, I.V. (Belarus): Canonical forms of linear nonstationary system
of equations and their applications.
Glaeske, H.-J. (Germany), together with Saigo, M. (Japan): On a hybrid
Laguerre Fourier transforms.
Grebennikov, E.A. (Russia), together with Kozak, D., and Yakubyak, M.
(Poland): KAM-theory and stability of homographic solutions of Hamiltonian
systems of cosmic dynamics.
Gromak, V.I. (Belarus): Isodromic deformation of linear systems and of
p-type equations.
Karapetyants, N.K.(Russia): On a fredholmness of a class of Hankel
operators.
Kilbas, A.A. (Belarus): Integral and differential equations of fractional
order. Theory and applications.
Korzyuk, V.I. (Belarus): Conjugation problems for differential equations
with integro-differential conditions.
Kun Soo Chang (Korea): Analytic Fourier-Feynman transform and convolution
of functionals on abstract Wiener space.
Laurinchikas, A. (Lithuania) - The Lerch zeta function.
Lebedev, A.V., together with Antonevich, A.B. and Bakhtin, V.I.
(Belarus): Variational principle for spectral radius.
Love, E.R. (Australia): Fourier-style expansions in series of general
Legendre functions.
Marichev, O.I., together with Trott, M. and Adamchik, V.S. (USA): The
mathematical functions in Mathematica.
Mitjushev, V.V. (Poland), together with Adler, P. (France): Boundary value
problems in a class of doubly periodic functions and their applications in
porous media.
Nakhushev, A.M., together with Nakhusheva, V.A. (Russia): On some
differential equations of fractional order and their applications.
Rogosin, S.V.(Belarus), together with Reissig, M.(Germany): Complex
Hele-Shaw model with linear and nonlinear kinetic undercooling
regularization.
Saitoh, S.(Japan): Various integral operators induced by integral
transforms.
Yurchuk, N.I.(Belarus): Regularization by nonlocal conditions of the
incorrect problems for the differential operator equations.
The 93 sectional talks were distributed as follows:
Integral Transforms and Special Functions (14);
Ordinary Differential equations (13);
Partial Differential Equations (13);
Different Aspects of Function Theory (12);
Applications of Differential Equations and Function Theory (15);
Integral and Functional Equations and Applications (13);
Operator Theory (13).
It is hoped that the Proceedings of AMADE will be published in
"Proceedings of Institute of Mathematics" of the Belarusian National
Academy of Sciences. Some of the reports will be published in a special
issue of "Integral Transforms and Special Functions", dedicated to
Professor Anatolii Platonovich Prudnikov (Russia) who was one of the main
founders of AMADE. Though his sudden death on January 10, 1999 was a big
tragedy, participants at the Conference honored his memory in their
reports.
Topic #10 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Andre Ronveaux
Subject: Report on Benin Workshop
The FIRST INTERNATIONAL WORKSHOP ON CONTEMPORARY PROBLEMS IN MATHEMATICAL
PHYSICS was held in Cotonou, Republique de BENIN from Oct 31st to Nov 7th,
1999.
About 100 participants from Africa, Europe and North America attended this
Workshop organized by the IMSP (Institut de Mathematiques et Sciences
Physiques in Porto-Novo,BENIN). Presentations included invited 50-minute
plenary talks (21), and 20-minute communications (36).
The following topics were covered in parallel sessions:
Coherent states, wavelets and geometric methods in theoretical physics.
Quantum field theory, atomic and molecular physics, Operator theory and
orthogonal polynomials. Being involved only in the last topic I can say
that the Operator theory part was devoted mainly to PDE and Integral
operators, presented more or less in the French tradition (Sobolev
spaces,numerical approximations etc...) but sometimes applied to African
needs. For instance, regulation of dams on the Senegal river and
transport problems in the Oueme river (Benin) motivated sophisticated
simulations with control theory coupled with fluid mechanics. Three
Lectures on Classical Orthogonal Polynomials (available on request) were
given by the author of this report, and other communications dealt with
some semi-classical families (generalized Charlier and Meixner),
Laguerre-Freud equations, Laguerre-Hahn class and numerical integration.
During the last day participants also had the opportunity to attend an
International Conference on Interuniversity Cooperation, under the
auspices of UNESCO.
We appreciated the efforts of the organizers to ensure the comfort of all
participants, and the relaxing outdoor discussions between lectures among
wonderful trees and flowers. Several banquets, receptions and excursions
also succeeded in creating a friendly ambience for which we are indebted
to the organizers. The proceedings will be published by World Scientific
(Editors: J.Govaerts, N.M.Hounkonnou and W.A.Lester,Jr) and the second
Workshop is already planned, again in Cotonou, in November 2001.
Topic #11 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Special issues of Methods and Applications of Analysis in honour
of Richard Askey
Richard Askey turned 65 in June 1998 and, some time before that, Mourad
Ismail and Dennis Stanton started to solicit articles for a special issue
of "Methods and Application of Analysis" in his honour. Dick had been on
the Editorial Board of the journal since its inception and had been for 20
years on the Editorial Board of SIAM Journal on Mathematical Analysis for
20 years before that. As the Special Issue Editors explain in a tribute
to Askey (Vol 6, no 1, March 1999), the response was overwhelming and so
far the articles received and accepted have filled nos 1 and 2 and others
are just now appearing in no 3.
Topic #12 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Changes at Methods and Applications of Analysis
The journal "Methods and Applications of Analysis" has new
Editors-in-Chief, Zhouping Xin (Courant Institute and Chinese University
of Hong Kong) and Shing-Tung Yau (Harvard University) replacing the
founding Editors-in-Chief, Roderick Wong and Robert Miura. Roderick and
Robert deserve the heartfelt thanks of the OP and SF community for their
service in providing such an excellent journal for the publication of work
in our areas and related parts of mathematics. In particular, Roderick
Wong took on and continued this work at the same time as he moved to the
City University of Hong Kong and undertook heavy administrative
responsibilities.
Information on the journal is maintained at the web site:
http://www.intlpress.com/journals/maa/index.html
Topic #13 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Wolfram Koepf
Subject: Review Of "Special Functions" by Andrews, Askey and Roy
[This item appeared in our printed Newsletter, October, 1999.]
Special Functions
By George E. Andrews, Richard Askey, Ranjan Roy
Encyclopedia of Mathematics and its Applications Vol. 71. Cambridge
University Press, Cambridge, 1999.
US$ 85.00, xvi, 664 pp., ISBN 0-521-62321-9.
This book covers a wealth of material on special functions, notably
knowledge which was developed by Richard Askey and his co-authors during
the several decades of his contributions to this subject, but also
material which connects special functions with combinatorial questions
collected by George Andrews. These two researchers are well-known for
their efforts to support and demand the use of hypergeometric functions in
their respective fields, hence hypergeometric functions and
q-hypergeometric functions (basic hypergeometric functions) play a
prominent role in the book under review. The book covers 12 chapters and 6
appendices. Furthermore, it contains a rich collection of 444 (!)
exercises that are distributed among the different chapters.
Here are the details:
Chapter 1: The Gamma and Beta Functions.
In this chapter the usual material about the Gamma and Beta functions is
covered. Moreover, results for the logarithmic derivative
psi(x)=Gamma'(x)/Gamma(x) of the Gamma function and for the Hurwitz and
Riemann zeta function are developed; in particular, several integral
representations are given. The Gamma function is characterized by the
Bohr-Mollerup theorem, and finally the p-adic Gamma function is
introduced.
Chapter 2: The Hypergeometric Functions.
The generalized hypergeometric function is introduced, and elementary
examples are given. Euler's integral representation, and the usual
summation theorems (Gauss, Chu-Vandermonde, Pfaff-Saalschutz, Dixon) come
next. Then the hypergeometric differential equation is treated from the
Riemannian point of view that analytic functions are determined to a large
extent by their singularities. Next, Barnes type integrals, contiguous
relations, and continued fractions of ratios of hypergeometric functions
are covered. The Jacobi polynomials as specific hypergeometric polynomials
are introduced. Finally, dilogarithms, binomial sums, and fractional
integration by parts are treated.
Chapter 3: Hypergeometric Transformations and Identities.
This chapter starts with quadratic transformations. Then elliptic
integrals are considered as hypergeometric functions, and
arithmetic-geometric mean sequences are introduced. Next, transformations
for balanced series, Whipple's transformation and Dougall's formula are
given. Integral analogs of hypergeometric sums lead to the Wilson
polynomials. The Riemannian point of view is reconsidered in connection
with quadratic transformations. Gosper's algorithm on indefinite
hypergeometric summation is given, and the Wilf-Zeilberger method for
proving hypergeometric identities is compared with Pfaff's method, and the
question of how these methods are related to contiguous relations is
analyzed.
Chapter 4: Bessel Functions and Confluent Hypergeometric Functions.
Here, the confluent hypergeometric function is introduced. Then a Barnes
type integral is given. As special cases, the Whittaker and the Bessel
functions are covered. Recurrence equations, integral representations, and
asymptotic expansions are treated. A two-dimensional Fourier transform
leads to a generating function of the Bessel functions. Addition theorems
and integrals of Bessel functions come next. Finally zeros and
monotonicity properties of Bessel functions are discussed.
Chapter 5: Orthogonal Polynomials.
The elementary properties of general orthogonal polynomials are derived.
Next, Gauss quadrature is examined. Then zeros of orthogonal polynomials
are discussed, and the connection of orthogonal polynomials with continued
fractions is treated. After Parseval's formula, the moment-generating
function is introduced.
Chapter 6: Special Orthogonal Polynomials.
Under this heading comes a discussion of the classical hypergeometric type
orthogonal polynomials. The Hermite, Laguerre and Jacobi polynomials and
their properties are discussed in detail. Then linearization coefficients
are considered, and combinatorial interpretations of the classical systems
are given. The Wilson polynomials and their properties come next. Finally
a q-generalization of the ultraspherical polynomials is deduced.
Chapter 7: Topics in Orthogonal Polynomials.
Connection coefficients are introduced, and for the classical systems
these coefficients are explicitly determined. Nonnegativity results for
hypergeometric functions and positive polynomial sums come next. In
particular, the Askey-Gasper inequality which was used by de Branges in
his proof of the Bieberbach conjecture [1] is deduced using results about
connection coefficients. Theorems by Vietoris and Turan are covered.
Finally, Apery's irrationality proof of zeta(3) is given.
Chapter 8: The Selberg Integral and Its Applications.
Here, Selberg's and Aomoto's integrals and extensions of these formulas
are given. A two-dimensional electrostatic problem studied by Stieltjes
connects the zeros of the Jacobi polynomials with Selberg's integral in an
interesting way. Siegel's inequality, which is a refinement of the
arithmetic-geometric mean inequality, is studied next, and a connection to
the Laguerre polynomials is considered. Applications of Selberg's integral
to constant-term identities and nearly-poised _3F_2 identities are given.
The Hasse-Davenport relation and a finite-field analog of Selberg's
integral finish this chapter.
Chapter 9: Spherical Harmonics.
Harmonic polynomials and the Laplace equation in three dimensions provide
an introduction to the topic of this chapter. Then the harmonic
polynomials of degree k and their orthogonality are studied. Their
addition theorem yields an addition theorem for ultraspherical polynomials
which was used by Weinstein [3] in his proof of the Bieberbach conjecture.
It is shown that Fourier transforms of higher order are still expressible
in terms of Bessel functions. Next, finite-dimensional representations of
compact groups are studied. Finally, Koornwinder's product formula for
Jacobi polynomials is given.
Chapter 10: Introduction to q-series.
In this chapter, the theory of q-hypergeometric series (basic
hypergeometric series) is motivated by considering non-commutative
q-algebra, related with the rule yx=qxy. Using this approach, the
definition of the q-binomial coefficients and their connection with the
standard binomial coefficients are straightforward. The q-integral is
defined, and the q-binomial theorem is proved by two different approaches
both based on recurrence equations. The q-Gamma function, and Jacobi's
triple product identity are next. Ramanujan's summation formula is used
to give results about the representations of numbers as sums of squares.
Elliptic and theta functions are covered, and q-beta integrals are used to
find a q-analog of the Wilson polynomials. Finally, the basic
hypergeometric series is studied. Basic hypergeometric identities, the
q-ultraspherical polynomials and the Mellin transform finish this chapter.
Chapter 11: Partitions.
Partitions are defined, and the connection of partition analysis with
q-series is studied. Generating functions, and other results on partitions
are obtained by this method. Next, graphical methods are discussed, and
congruence properties of partitions are covered.
Chapter 12: Bailey Chains.
Rogers's second proof of the Rogers-Ramanujan identities is given. Then,
Bailey's lemma and Watson's transformation formula are treated. Finally,
some applications are given.
Appendices on Infinite Products, Summability and Fractional Integration,
Asymptotic Expansions, Euler-Maclaurin Summation Formula, Lagrange
Inversion Formula, and Series Solutions of Differential Equation follow,
and a bibliography, an index, a subject index and a symbol index complete
the book.
To begin with these last items: For a book of this size, the subject index
is rather small (3 pages). Hence, obviously not every subject can be found
here. Just to mention a few, one finds neither "addition theorem", nor
"Bieberbach conjecture", nor "irrationality of zeta(3)", nor "indicial
equation" (notation defined on p. 640 in Appendix F, and used on p. 74).
Many other topics cannot be found in the subject index either. In my
opinion, a book covering such a wealth of information needs a better
index. Similarly, the bibliography (on purpose) contains only the articles
that are explicitly mentioned in the text, and by no means covers the
topic of the book encyclopedically. Another minor irritation is the fact
that the notations [x] (e.g. on pp. 203, 314) and lfloor x rfloor (e.g. on
pp. 279, 340) for the greatest integer in x are used synonymously, but
only the latter is defined on p 15.
On the other hand, the material is written in an excellent manner, and it
gives the reader very interesting insights to special functions. On many
occasions, theorems are proved by several alternative methods. This gives
the reader a much better feeling for what is going on, indicating that
Special Functions is not a topic which can be taught deductively.
Furthermore, the book contains very few typos.
But a book of this size covers thousands of formulas, and by Murphy's law,
a few of them should be incorrect. I tried to find such misprints, in
particular in the sections 3.11 and 3.12 about summation methods, since
there I could use my Maple software for purposes of detection [2]. Not
surprisingly, this search was successful: Formula (3.11.10) is incorrect
by a factor -n; both identities in the middle of p. 175 are incorrect
restatements of the corresponding contiguous relations (3.11.12) and
(3.11.15) on p. 173; furthermore, in formula (3.12.1) the upper
parameter z+n-1 should read z+n+1. (I would like to thank George Andrews
for sending me the corrected formula.)
In spite of these minor shortcomings, I recommend this book warmly as a
rich source of information to everybody who is interested in Special
Functions.
References
[1] de Branges, L.: A proof of the Bieberbach conjecture. Acta Math. 154,
1985, 137--152.
[2] Koepf, Wolfram: Hypergeometric Summation. An Algorithmic Approach to
Summation and Special Function Identities. Vieweg,
Braunschweig/Wiesbaden, 1998.
[3] Weinstein, L.: The Bieberbach conjecture. Int. Math. Res. Not. 5,
1991, 61--64.
Topic #14 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Tom Koornwinder
Subject: Doron Zeilberger's Maple Packages and Programs
The following is from the web site:
http://www.math.temple.edu/~zeilberg/programs.html
EKHAD, a Maple package for proving binomial coefficients and other types
of identities. To use it, download it as EKHAD, go into Maple, type `read
EKHAD:`, and follow the instructions given there. Version of Feb. 25,
1999. This new version benefited from a GREAT SUGGESTION of Frederic
CHYZAK (whom we thank so much!), and now is roughly four times as fast. It
may not work on very early versions of Maple, in which case you still use
the Old Version of EKHAD.
qEKHAD, a Maple package for proving q-binomial coefficients (a.k.a.
basic-hypergeometric, and q-) identities. To use it, download it as
qEKHAD, go into Maple, type `read qEKHAD:`, and follow the instructions
given there. Version of July 20, 1999. The new version implements the
above suggestion of Frederic CHYZAK, but the speed-up is not so dramatic.
If you have a very early versions of Maple, you may need the Old Version
of qEKHAD.
Topic #15 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Ernst Davidovich Krupnikov
Subject: Question on Schrodinger equations
What are all the Schrodinger equations that have exact solutions
expressible in terms of the Kampe de Feriet function?
Topic #16 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: Allison Bogardo
Subject: SIAM Student Paper Prizes
SIAM Student Paper Prizes
The annual SIAM Student Paper Prizes will be awarded during the 2000
SIAM Annual Meeting, July 10-14, at the Westin Rio Mar Beach Resort
in Rio Grande, Puerto Rico.
If you are a student or know of a student who would like to take part
in the competition, here are the details:
The authors of the three best papers in applied and computational
mathematics written by students and submitted to SIAM will receive a
$1,000 cash prize and a framed calligraphed certificate as well as
gratis registration for the meeting. There is no provision for
travel expenses associated with the prize.
Papers must be singly authored and not previously published or
submitted for publication to be eligible for consideration. To
qualify, authors must be students in good standing who have not
received their PhDs at the time of submission.
In submitting their work for publication, authors are asked to
consider SIAM journals. However, student paper prize winners are not
guaranteed publication in any SIAM journal; all papers submitted to
SIAM journals are subject to the same refereeing process and
standards.
Submissions must be received in the SIAM office before
February 15, 2000.
Submissions, which must be in English, can be sent by regular mail or
fax. Each submission must include (1) an extended abstract NOT
LONGER THAN 5 PAGES (including bibliography); (2) the complete
paper, which will be used solely for clarification of any questions;
(3) a statement by the student's faculty advisor that the paper has been
prepared by the author indicated and that the author is a student in
good standing; (4) a letter by the student's faculty advisor
describing and evaluating the paper's contribution; and (5) a short
biography of the student.
Submissions will be judged on originality, significance, and quality
of exposition.
The winners will be notified by April 15, 2000.
Please direct your submission and any questions you may have to
A. Bogardo at SIAM, 3600 University City Science Center,
Philadelphia, PA 19104-2688; telephone (215) 382-9800; e-mail to
bogardo@siam.org.
Topic #17 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: OP-SF preprints in xxx archive
The following preprints related to the field of orthogonal
polynomials and special functions were recently posted or cross-listed to
one of the subcategories of the xxx archives. See:
http://front.math.ucdavis.edu/math.CA
http://front.math.ucdavis.edu/math.CO
http://front.math.ucdavis.edu/math.QA
http://xxx.lanl.gov/archive/solv-int
E-print math.QA/0001033
Title: Askey-Wilson polynomials: an affine Hecke algebraic approach
Authors: Masatoshi Noumi, Jasper V. Stokman
Categories: QA Quantum Algebra (CA Classical Analysis; RT Representation
Theory)
Math Subject Class: 33D45, 33D80
Comments: 35 pages
Abstract: We study Askey-Wilson type polynomials using representation
theory of the double affine Hecke algebra. In particular, we prove
bi-orthogonality relations for non-symmetric and anti-symmetric
Askey-Wilson polynomials with respect to a complex measure. We give
duality properties of the non-symmetric Askey-Wilson polynomials, and we
show how the non-symmetric Askey-Wilson polynomials can be created from
Sahi's intertwiners. The diagonal terms associated to the bi-orthogonality
relations (which replace the notion of quadratic norm evaluations for
orthogonal polynomials) are expressed in terms of residues of the complex
weight function using intertwining properties of the non-symmetric
Askey-Wilson transform under the action of the double affine Hecke
algebra. We evaluate the constant term, which is essentially the
well-known Askey-Wilson integral, using shift operators. We furthermore
show how these results reduce to well-known properties of the symmetric
Askey-Wilson polynomials, as were originally derived by Askey and Wilson
using basic hypergeometric series theory.
From: Jasper V. Stokman
Date: Thu 6 Jan 2000 11:49:54 GMT
E-print math.CA/9912149
Title: A remark on perturbations of sine and cosine sums
Author: Mihail N. Kolountzakis
Categories: CA Classical Analysis
Math Subject Class: 42A05
Comments: 2 pages
Abstract: Consider a collection $\lambda_1<...<\lambda_N$ of distinct
positive integers and the quantities $$ M_1 = M_1(\lambda_1,...,\lambda_N)
= \max_{0\le x \le 2\pi} |\sum_{j=1}^N \sin{\lambda_j x}| $$ and $$ M_2 =
M_2(\lambda_1,...,\lambda_N) = - \min_{0\le x \le 2\pi}
\sum_{j=1} \cos{\lambda_j x}. $$ Prompted by a discussion with G. Benke
we prove that collections of frequencies $\lambda_j$ which have $M_1 =
o(N)$ or $M_2 = o(N)$ are unstable, in the sense that one can perturb the
$\lambda_j$ by one each and get $M_1 \ge c N$ and $M_2 \ge c N$.
From: Mihail N. Kolountzakis
Date: Sat 18 Dec 1999 10:39:21 GMT
E-print math.CA/9912140
Title: The Askey-Wilson function transform scheme
Authors: Erik Koelink, Jasper V. Stokman
Categories: CA Classical Analysis (QA Quantum Algebra)
Math Subject Class: 33D15, 33D45 (Primary) 33D80 (Secondary)
Comments: 17 pages, 2 figures, AMS-TeX Some formulas corrected,
reference updated
Abstract: In this paper we present an addition to Askey's scheme of
q-hypergeometric orthogonal polynomials involving classes of q-special
functions which do not consist of polynomials only. The special functions
are q-analogues of the Jacobi and Bessel function, and are Askey-Wilson
functions, big q-Jacobi functions and little q-Jacobi functions and the
corresponding q-Bessel functions. The generalised orthogonality relations
and the second order q-difference equations for these families are given.
Limit transitions between these families are discussed. The quantum group
theoretic interpretations are discussed shortly.
From: Erik Koelink
Date: Fri 17 Dec 1999 14:52:03 GMT
Revised: Thu 23 Dec 1999 13:57:36 GMT
E-print math.CA/9912113
Title: On the q-convolution on the line
Author: Giovanna Carnovale
Categories: CA Classical Analysis (QA Quantum Algebra)
Math Subject Class: 33D80; 33D15; 42A85 (primary); 17B37 (secondary)
Report number: 33/99
Abstract: I continue the investigation of a q-analogue of the convolution on
the line started in a joint work with Koornwinder and based on a formal
definition due to Kempf and Majid.
Two different ways of approximating functions by means of the
convolution and convolution of delta functions are introduced. A new family of
functions that forms an increasing chain of algebras depending on a
parameter s > 0 is constructed. The value of the parameter for which the
mentioned algebras are well behaved, commutative and unital is found. In
particular a privileged algebra of functions belonging to the above family is
shown to be the quotient of an algebra studied in the previous article modulo
the kernel of a q-analogue of the Fourier transform. This result has an
analytic interpretation in terms of analytic functions whose q-moments have a
particular behaviour. The same result makes it possible to extend results on
invertibility of the q-Fourier transform due to Koornwinder. A few results on
invertibility of functions with respect to the q-convolution are also obtained
and they are related to solving certain simple linear q-difference equations
with polynomial coefficients.
From: carnoval
Date: Wed 15 Dec 1999 09:38:09 GMT
E-print math-ph/9912020
Title: One Dimensional Regularizations of the Coulomb Potential with
Application to Atoms in Strong Magnetic Fields
Authors: Raymond Brummelhuis, Mary Beth Ruskai, Elisabeth Werner
Categories: MP Mathematical Physics (CA Classical Analysis)
Math Subject Class: 81V45, 33E20
Journal reference: Differential Equations and Mathematical Physics, ed.
by G. Weinstein and R. Weikard, pp. 43-51 (International Press, 2000)
Comments: 9 pages, Proceedings of a conference on Differential
Equations and Mathematical Physics at University of Alabama Birmingham
(March 1998)
Abstract: We consider one-dimensional regularizations of the Coulomb
potential formed by taking a two-dimensional expectation of the Coulomb
potential with respect to the Landau states. It is well-known that such
functions arises naturally in the study of atoms in strong magnetic
fields. For many-electron atoms consideration of the Pauli principle
requires convex combinations of such potentials and interactions in which
the regularizations also contain a 2^{-1/2} rescaling. We summarize the
results of a comprehensive study of these functions including recursion
relations, tight bounds, convexity properties, and connections with
confluent hypergeometric functions. We also report briefly on their
application in one-dimensional models of many-electrons atoms in strong
magnetic fields.
From: Mary Beth Ruskai
Date: Tue 28 Dec 1999 06:40:19 GMT
E-print math.PR/9912170
Title: Probability laws related to the Jacobi theta and Riemann zeta function
and Brownian excursions
Authors: P. Biane, J. Pitman, M. Yor
Categories: PR Probability Theory (CA Classical Analysis)
Math Subject Class: 11M06; 60J65; 60E07
Report number: DMA-99-30
Comments: LaTeX; 40 pages; review paper
Abstract: This paper reviews known results which connect Riemann's
integral representations of his zeta function, involving Jacobi's theta
function and its derivatives, to some particular probability laws
governing sums of independent exponential variables. These laws are
related to one-dimensional Brownian motion and to higher dimensional
Bessel processes. We present some characterizations of these probability
laws, and some approximations of Riemann's zeta function which are related
to these laws.
From: Biane
Date: Tue 21 Dec 1999 11:18:04 GMT
E-print math.QA/9911163
Title: Fourier transforms on the quantum SU(1,1) group
Authors: Erik Koelink, Jasper Stokman, Mizan Rahman (appendix)
Categories: QA Quantum Algebra (CA Classical Analysis)
Math Subject Class: 17B37, 33D55, 33D80 (Primary) 43A32, 43A90, 46L89,
47B15 (Secondary)
Comments: 77 pages, 1 figure
Abstract: The main goal is to interpret the Askey-Wilson function and the
corresponding transform pair on the quantum SU(1,1) group. A weight on the
C^*-algebra of continuous functions vanishing at infinity on the quantum
SU(1,1) group is studied, which is left and right invariant in a weak
sense with respect to a product defined using Wall functions. The Haar
weight restricted to certain subalgebras are explicitly determined in
terms of an infinitely supported Jackson integral and in terms of an
infinitely supported Askey-Wilson type measure. For the evaluation the
spectral analysis of explicit unbounded doubly infinite Jacobi matrices
and some new summation formulas for basic hypergeometric series are
needed. The spherical functions are calculated in terms of Askey-Wilson
functions and big q-Jacobi functions. The corresponding spherical Fourier
transforms are identified with special cases of the big q-Jacobi function
transform and of the Askey-Wilson function transform.
From: Erik Koelink
Date: Mon 22 Nov 1999 11:05:06 GMT
E-print math.CO/9912093
Title: Riemann-Hilbert problem and the discrete Bessel kernel
Author: Alexei Borodin
Categories: CO Combinatorics (MP Mathematical Physics)
Comments: AMSTeX, 17 pages
Abstract: We use discrete analogs of Riemann-Hilbert problem's methods to
derive the discrete Bessel kernel which describes the poissonized
Plancherel measures for symmetric groups. To do this we define a discrete
analog of 2 by 2 Riemann-Hilbert problems of special type. We also give an
example, explicitly solvable in terms of classical special functions, when
a discrete Riemann-Hilbert problem converges in a certain scaling limit to
a conventional one; the example originates from the representation theory
of the infinite symmetric group.
From: Alexei Borodin
Date: Sun 12 Dec 1999 17:46:39 GMT
E-print math.CO/9912052
Title: Restricted permutations, continued fractions, and Chebyshev
polynomials
Authors: T. Mansour, A. Vainshtein
Categories: CO Combinatorics
Abstract: Let f_n^r(k) be the number of 132-avoiding permutations on n
letters that contain exactly r occurrences of 12... k, and let F_r(x;k)
and F(x,y;k) be the generating functions defined by $F_r(x;k)=\sum_{n\gs0}
f_n^r(k)x^n$ and $F(x,y;k)=\sum_{r\gs0}F_r(x;k)y^r$. We find an explicit
expression for F(x,y;k) in the form of a continued fraction. This allows
us to express F_r(x;k) for $1\ls r\ls k$ via Chebyshev polynomials of the
second kind.
From: Toufik Mansour
Date: Mon 6 Dec 1999 22:55:37 GMT
E-print math.QA/9912094
Title: Ubiquity of Kostka polynomials
Author: Anatol N. Kirillov
Categories: QA Quantum Algebra (CO Combinatorics)
Comments: LaTeX, 60 pages, some typos corrected, and new exercises added
Abstract: We report about results revolving around Kostka-Foulkes and
parabolic Kostka polynomials and their connections with Representation
Theory and Combinatorics. It appears (see Section 7) that the set of all
parabolic Kostka polynomials forms a semigroup, which we call Liskova
semigroup. We show that polynomials frequently appearing in Representation
Theory and Combinatorics belong to the Liskova semigroup. Among such
polynomials we study rectangular q-Catalan numbers; generalized exponents
polynomials; principal specializations of the internal product of Schur
functions; generalized q-Gaussian polynomials; parabolic Kostant
partition function and its q-analog; certain generating functions on the
set of transportation matrices. In each case we apply rigged
configurations technique to obtain some interesting information about
Kostka-Foulkes polynomials, Kostant partition function, MacMahon,
Gelfand-Tsetlin and Chan-Robbins polytopes. We study also some properties
of l-restricted generalized exponents and the stable behaviour of certain
Kostka-Foulkes polynomials.
From: Anatol N. Kirillov
Date: Sun 12 Dec 1999 15:08:55 GMT
Revised: Mon 27 Dec 1999 06:48:47 GMT
E-print math.AG/9911030
Title: Rational Hypergeometric Functions
Authors: Eduardo Cattani, Alicia Dickenstein, Bernd Sturmfels
Categories: AG Algebraic Geometry (CO Combinatorics)
Report number: MSRI 1999-051
Comments: LaTeX, 26 pages
Abstract: Multivariate hypergeometric functions associated with toric
varieties were introduced by Gel'fand, Kapranov and Zelevinsky.
Singularities of such functions are discriminants, that is, divisors
projectively dual to torus orbit closures. We show that most of these
potential denominators never appear in rational hypergeometric functions.
We conjecture that the denominator of any rational hypergeometric function
is a product of resultants, that is, a product of special discriminants
arising from Cayley configurations. This conjecture is proved for toric
hypersurfaces and for toric varieties of dimension at most three. Toric
residues are applied to show that every toric resultant appears in the
denominator of some rational hypergeometric function.
From: Eduardo Cattani
Date: Thu 4 Nov 1999 22:23:38 GMT
nlin.SI/0001001
From: Dmitri Scherbin
Date: Thu, 6 Jan 2000 22:32:36 GMT (16kb)
Fermionic representation for basic hypergeometric functions related to
Schur polynomials
Authors: A.Yu.Orlov, D.M.Scherbin
Subj-class: Exactly Solvable and Integrable Systems
We present the fermionic representation for the q-deformed
hypergeometric functions related to Schur polynomials. For q=1
it is known that these hypergeometric functions are related to
zonal spherical polynomials for GL(N,C)/U(N) symmetric space.
Multivariable hypergeometric functions appear to be
tau-functions of the KP and of the two-dimensional Toda lattice
hierarchies. The variables of the hypergeometric functions are
the higher times of those hierarchies. The discrete Toda lattice
variable shifts parameters of hypergeometric functions.
math-ph/0001003
From: Aleksandar Mikovic
Date: Mon, 3 Jan 2000 12:22:33 GMT (9kb)
Matrix Factorization for an SO(2) Spinning Top and Related Problems
Authors: Aleksandar Mikovic
Comments: 11 pages, Latex
Subj-class: Mathematical Physics; Exactly Solvable and Integrable Systems
We study the matrix factorization problem associated with an
SO(2) spinning top by using the algebro-geometric approach.
We derive the explicit expressions in terms of Riemann theta
functions and discus some related problems including a
non-compact extension and the case when the Lax matrix
contains higher-order powers of the spectral parameter.
solv-int/9912006
From: Dimitri Kusnezov
Date: Mon, 6 Dec 1999 20:00:52 GMT (158kb)
Group Theoretical Properties and Band Structure of the Lame Hamiltonian
Authors: Hui Li, Dimitri Kusnezov, Francesco Iachello
Comments: 21 pages Revtex + 6 eps + 2 jpg figures
Subj-class: Exactly Solvable and Integrable Systems
We study the group theoretical properties of the Lame equation
and its relation to su(1,1) and su(2). We compute the band
structure, dispersion relation and transfer matrix and discuss the
dynamical symmetry limits.
Topic #18 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Changes of Address, WWW Pages, etc
The URL of Margit Roesler's home page has changed to
http://pckoenig7.mathematik.tu-muenchen.de/~roesler/
Dr. Semyon Yakubovich (Technishe Universiteit Eindhoven, Netherlands) has
been appointed as a Visiting Associate Professor at the University of
Porto (Portugal) starting February 2000. His address will be:
Departamento de Matematica Pura
Faculdade de Ciencias
Universidade do Porto
Praca a gomes Teixeira
4099-002 Porto Portugal
Luc Vinet has been appointed Vice-Principal (Academic) at McGill
University, Montreal, Canada. His e-mail address is:
Vinet@vps.mcgill.ca
Topic #19 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Subscribing to OP-SF NET
There are two ways to subscribe to OP-SF NET:
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Topic #20 ------------ OP-SF NET 7.1 ----------- January 15, 2000
~~~~~~~~~~~~~
From: OP-SF NET Editor
Subject: Obtaining back issues of OP-SF NET and submitting contributions
to OP-SF NET and Newsletter
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Martin Muldoon, Webmaster and OP-SF NET editor
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