The Askey-Wilson function transform
Classical Analysis and ODEs
2010-11-03 v1 Quantum Algebra
Representation Theory
Abstract
In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform, which is given explicitly in terms of basic hypergeometric series, thus generalizes the Jacobi function as well as the Bessel function. The kernel is named the Askey-Wilson function, since it provides an analytical continuation of the Askey-Wilson polynomial in its degree. In this paper we establish the -theory of the Askey-Wilson function transform, and we explicitely determine its inversion formula.
Cite
@article{arxiv.math/0004053,
title = {The Askey-Wilson function transform},
author = {Erik Koelink and Jasper V. Stokman},
journal= {arXiv preprint arXiv:math/0004053},
year = {2010}
}
Comments
LaTeX2e file. 19 pages