The program of the afternoon is as follows:
14.00-14.45
Wolter Groenevelt (Institute of Applied Mathematics,
Delft University of Technology),
A Hecke algebra approach to Wilson polynomials and Wilson functions
15.00-15.45
Natig Atakishiyev
(IIMAS-Cuernavaca, Universidad Nacional Autónoma de México),
On integral and finite Fourier transforms of
continuous q-Hermite polynomials of Rogers
16.00-16.45
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
Abstract Groenevelt
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.
Abstract Atakishiyev
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.