The program of the afternoon is as follows:
Wolter Groenevelt (Institute of Applied Mathematics,
Delft University of Technology),
A Hecke algebra approach to Wilson polynomials and Wilson functions
(IIMAS-Cuernavaca, Universidad Nacional Autónoma de México),
On integral and finite Fourier transforms of continuous q-Hermite polynomials of Rogers
Fokko van de Bult (KdV Institute, University of Amsterdam),
The symmetries of the 2φ1
Location: Room P.015B, Euclides building, Plantage Muidergracht 24, Amsterdam
Date and time: Wednesday April 16, 2008, 14.00-17.00 hour
Information: Tom Koornwinder
Cherednik's double affine Hecke algebras provide an algebraic structure that explains many fundamental properties of the Macdonald polynomials and Koornwinder polynomials. In this talk I explain how Wilson polynomials and Wilson functions (in one variable) fit into a similar algebraic framework.
We give an overview of the remarkably simple transformation properties of the continuous q-Hermite polynomials of Rogers with respect to the classical Fourier integral transform. The behavior of the q-Hermite polynomials under the finite Fourier transform and an explicit form of the q-extended eigenfunctions of the finite Fourier transform, defined in terms of these polynomials, are also discussed.
Abstract van de Bult
It is well-known that the 2φ1 satisfies the Heine transformation formulas. It is generally assumed these are the only transformations relating a 2φ1 with general parameters to another 2φ1. We will give a proof that Heine's transformations are indeed all possible transformations (and of course first define what we mean by this statement). An important idea in the proof is the philosophy that a function is almost completely determined by the q-difference equations it satisfies.