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Askey-Wilson polynomials for root systems of type BC
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 itExpand
Jacobi Functions and Analysis on Noncompact Semisimple Lie Groups
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 atExpand
Two-Variable Analogues of the Classical Orthogonal Polynomials
Publisher Summary This chapter discusses two-variable analogues of the classical orthogonal polynomials. Analogues in severable variables of the Jacobi polynomials are be highly nontrivialExpand
The convolution structure for Jacobi function expansions
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 structureExpand
On q-analogues of the Fourier and Hankel transforms
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
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 KoornwinderExpand
CQG algebras: A direct algebraic approach to compact quantum groups
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 theExpand
Orthogonal polynomials with weight function $(1-x)sp{alpha }(1+x)sp+Mdelta (x+1)+Ndelta (x-1)$
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 F3Expand
Askey-Wilson polynomials as zonal spherical functions on the SU (2) quantum group
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 ofExpand