English

A right inverse of the Askey-Wilson operator

Classical Analysis and ODEs 2009-09-25 v1

Abstract

We establish an integral representation of a right inverse of the Askey-Wilson finite difference operator on L2L^2 with weight (1x2)1/2(1-x^2)^{-1/2}. The kernel of this integral operator is ϑ4/ϑ4\vartheta'_4/\vartheta_4 and is the Riemann mapping function that maps the open unit disc conformally onto the interior of an ellipse.

Keywords

Cite

@article{arxiv.math/9310219,
  title  = {A right inverse of the Askey-Wilson operator},
  author = {B. Malcolm Brown and Mourad E. H. Ismail},
  journal= {arXiv preprint arXiv:math/9310219},
  year   = {2009}
}