A solution to the Al-Salam–Chihara moment problem

Wolter Groenevelt

doi:10.1007/978-3-030-10850-2_11

A solution to the Al-Salam–Chihara moment problem

Wolter Groenevelt^*

^*Corresponding author for this work

Analysis

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific

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.

Original language	English
Title of host publication	Positivity and Noncommutative Analysis
Subtitle of host publication	Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday
Editors	G. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven, A. Wickstead
Place of Publication	Cham
Publisher	Springer
Pages	223-248
Number of pages	26
ISBN (Electronic)	978-3-030-10850-2
ISBN (Print)	978-3-030-10849-6
DOIs	https://doi.org/10.1007/978-3-030-10850-2_11
Publication status	Published - 2019

Publication series

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

Keywords

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

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10.1007/978-3-030-10850-2_11

Cite this

Groenevelt, W. (2019). A solution to the Al-Salam–Chihara moment problem. In G. Buskes, M. de Jeu, P. Dodds, A. Schep, F. Sukochev, J. van Neerven, & A. Wickstead (Eds.), Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday (pp. 223-248). (Trends in Mathematics). Springer. https://doi.org/10.1007/978-3-030-10850-2_11

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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.",

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

author = "Wolter Groenevelt",

year = "2019",

doi = "10.1007/978-3-030-10850-2_11",

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Groenevelt, W 2019, A solution to the Al-Salam–Chihara moment problem. in G Buskes, M de Jeu, P Dodds, A Schep, F Sukochev, J van Neerven & A Wickstead (eds), Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday. Trends in Mathematics, Springer, Cham, pp. 223-248. https://doi.org/10.1007/978-3-030-10850-2_11

A solution to the Al-Salam–Chihara moment problem. / Groenevelt, Wolter.
Positivity and Noncommutative Analysis: Festschrift in Honour of Ben de Pagter on the Occasion of his 65th Birthday. ed. / G. Buskes; M. de Jeu; P. Dodds; A. Schep; F. Sukochev; J. van Neerven; A. Wickstead. Cham: Springer, 2019. p. 223-248 (Trends in Mathematics).

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific

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N2 - 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.

AB - 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.

KW - Indeterminate moment problem

KW - Little q-Jacobi function transform

KW - Q-Hypergeometric difference operator

KW - Q-Al-Salam–Chihara polynomials

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A solution to the Al-Salam–Chihara moment problem

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