A solution to the Al-Salam–Chihara moment problem
Book Chapter
(2019)
Author(s)
Wolter Groenevelt (TU Delft - Analysis)
Research Group
Analysis
DOI related publication
https://doi.org/10.1007/978-3-030-10850-2_11
To reference this document use:
https://resolver.tudelft.nl/uuid:2b0f1e37-0400-414d-99ad-aed86d4388bc
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Publication Year
2019
Language
English
Research Group
Analysis
Pages (from-to)
223-248
ISBN (print)
978-3-030-10849-6
ISBN (electronic)
978-3-030-10850-2
Abstract
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.
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