A solution to the Al-Salam–Chihara moment problem

Wolter Groenevelt*

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific


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

Original languageEnglish
Title of host publicationPositivity and Noncommutative Analysis
Subtitle of host publicationFestschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday
EditorsG. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven, A. Wickstead
Place of PublicationCham
Number of pages26
ISBN (Electronic)978-3-030-10850-2
ISBN (Print)978-3-030-10849-6
Publication statusPublished - 2019

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X


  • Indeterminate moment problem
  • Little q-Jacobi function transform
  • Q-Hypergeometric difference operator
  • Q-Al-Salam–Chihara polynomials


Dive into the research topics of 'A solution to the Al-Salam–Chihara moment problem'. Together they form a unique fingerprint.

Cite this