The Askey-Wilson polynomials and q-Sturm-Lioville problems
Classical Analysis and ODEs
2016-09-06 v1
Abstract
We find the adjoint of the Askey-Wilson divided difference operator with respect to the inner procuct on L^2(-1,1,(1-x^2)^-1/2 dx) defined as a Cauchy principle value and show that the Askey-Wilson polynomials are solutions of a q-Sturm-Liouville problem. From these facts we deduce various properties of the polynomials in a simple and straightforward way. We also provide an operator theoretic description of the Askey-Wilson operator.
Cite
@article{arxiv.math/9408209,
title = {The Askey-Wilson polynomials and q-Sturm-Lioville problems},
author = {B. Malcolm Brown and William Desmond Evans and Mourad E. H. Ismail},
journal= {arXiv preprint arXiv:math/9408209},
year = {2016}
}