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arXiv · 1812.01282

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

Wolter Groenevelt
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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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Wolter Groenevelt. 2018-12-04. A solution to the Al-Salam--Chihara moment problem. https://doi.org/10.1007/978-3-030-10850-2_11

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