English

A solution to the Al-Salam--Chihara moment problem

Classical Analysis and ODEs 2021-03-29 v1

Abstract

We study the qq-hypergeometric difference operator LL on a particular Hilbert space. In this setting LL can be considered as an extension of the Jacobi operator for q1q^{-1}-Al-Salam--Chihara polynomials. Spectral analysis leads to unitarity and an explicit inverse of a qq-analog of the Jacobi function transform. As a consequence a solution of the Al-Salam--Chihara indeterminate moment problem is obtained.

Cite

@article{arxiv.1812.01282,
  title  = {A solution to the Al-Salam--Chihara moment problem},
  author = {Wolter Groenevelt},
  journal= {arXiv preprint arXiv:1812.01282},
  year   = {2021}
}

Comments

22 pages

R2 v1 2026-06-23T06:30:42.866Z