English

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 L2L^2-theory of the Askey-Wilson function transform, and we explicitely determine its inversion formula.

Keywords

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