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Askey-Wilson polynomials for root systems of type BC

- T. Koornwinder
- Mathematics
- 1991

This paper introduces a family of Askey-Wilson type orthogonal polynomials in n variables associated with a root system of type BCn. The family depends, apart from q, on 5 parameters. For n = 1 it… Expand

BASIC HYPERGEOMETRIC SERIES (Encyclopedia of Mathematics and its Applications)

- T. Koornwinder
- Mathematics
- 1 May 1991

Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups

- T. Koornwinder
- Mathematics
- 1984

A Jacobi function \({\phi _\lambda }^{\left( {\alpha ,\beta } \right)}\left( {\alpha ,\beta ,\lambda \in C,\alpha \ne - 1, - 2,...} \right)\) is defined as the even C∞-function on ℝ which equals 1 at… Expand

Two-Variable Analogues of the Classical Orthogonal Polynomials

- T. Koornwinder
- Mathematics
- 1975

Publisher Summary
This chapter discusses two-variable analogues of the classical orthogonal polynomials. Analogues in severable variables of the Jacobi polynomials are be highly nontrivial… Expand

The convolution structure for Jacobi function expansions

- M. Flensted-jensen, T. Koornwinder
- Mathematics
- 1 December 1973

The product ϕλ(α,β)(t1)ϕλ(α,β)(t2) of two Jacobi functions is expressed as an integral in terms of ϕλ(α,β)(t3) with explicit non-negative kernel, when α≧β≧−1/2. The resulting convolution structure… Expand

On q-analogues of the Fourier and Hankel transforms

- T. Koornwinder, Rene F. Swarttouw
- Mathematics
- 13 August 2012

For H. Exton's q-analogue of the Bessel function (going back to W. Hahn in a special case, but different from F. H. Jackson's q-Bessel functions) we derive Hansen-Lommel type orthogonality relations,… Expand

A new proof of a Paley—Wiener type theorem for the Jacobi transform

- T. Koornwinder
- Mathematics
- 1 December 1975

which generalizes the Mehler-Fok transform, was studied by Titchmarsh [23, w 17], Olevskii [21], Braaksma and Meulenbeld [2], Flensted--Jensen [9], [11, w and w and Flensted--Jensen and Koornwinder… Expand

CQG algebras: A direct algebraic approach to compact quantum groups

- M. Dijkhuizen, T. Koornwinder
- Physics, Mathematics
- 8 June 1994

The purely algebraic notion of CQG algebra (algebra of functions on a compact quantum group) is defined. In a straightforward algebraic manner, the Peter-Weyl theorem for CQG algebras and the… Expand

Orthogonal polynomials with weight function $(1-x)sp{alpha }(1+x)sp+Mdelta (x+1)+Ndelta (x-1)$

- T. Koornwinder
- Mathematics
- 1 June 1984

We study orthogonal polynomials for which the weight function is a linear combination of the Jacobi weight function and two delta functions at 1 and — 1. These polynomials can be expressed as 4 F3… Expand

Askey-Wilson polynomials as zonal spherical functions on the SU (2) quantum group

- T. Koornwinder
- Mathematics
- 1 May 1993

On the $SU(2)$ quantum group the notion of (zonal) spherical element is generalized by considering left and right invariance in the infinitesimal sense with respect to twisted primitive elements of… Expand

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