A solution to the Al-Salam–Chihara moment problem

Groenevelt, W.G.M.

A solution to the Al-Salam–Chihara moment problem

Book chapter (2019)

Authors

W.G.M. Groenevelt Analysis -

Research Group

Analysis () (TU Delft)

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

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Published Date

2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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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