Harmonic Analysis on Quantum Complex Hyperbolic Spaces

In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order q-difference operator, whose eigenfunctions are related to the Al-Salam-Chihara po...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2011
Main Authors: Bershtein, O., Kolisnyk, Y.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147404
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Harmonic Analysis on Quantum Complex Hyperbolic Spaces / O. Bershtein, Y. Kolisnyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 21 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-147404
record_format dspace
spelling Bershtein, O.
Kolisnyk, Y.
2019-02-14T17:45:02Z
2019-02-14T17:45:02Z
2011
Harmonic Analysis on Quantum Complex Hyperbolic Spaces / O. Bershtein, Y. Kolisnyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 21 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 17B37; 20G42; 81R50; 33D45; 42C10
DOI: http://dx.doi.org/10.3842/SIGMA.2011.078
https://nasplib.isofts.kiev.ua/handle/123456789/147404
In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order q-difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it.
This paper is a contribution to the Special Issue “Relationship of Orthogonal Polynomials and Special Functions with Quantum Groups and Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/OPSF.html. This project started out as joint work with L. Vaksman and D. Shklyarov. We are grateful to both of them for helpful discussions and drafts with preliminary definitions and computations. Also we are grateful for referees for their comments that help to improve and simplify our exposition.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Harmonic Analysis on Quantum Complex Hyperbolic Spaces
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Harmonic Analysis on Quantum Complex Hyperbolic Spaces
spellingShingle Harmonic Analysis on Quantum Complex Hyperbolic Spaces
Bershtein, O.
Kolisnyk, Y.
title_short Harmonic Analysis on Quantum Complex Hyperbolic Spaces
title_full Harmonic Analysis on Quantum Complex Hyperbolic Spaces
title_fullStr Harmonic Analysis on Quantum Complex Hyperbolic Spaces
title_full_unstemmed Harmonic Analysis on Quantum Complex Hyperbolic Spaces
title_sort harmonic analysis on quantum complex hyperbolic spaces
author Bershtein, O.
Kolisnyk, Y.
author_facet Bershtein, O.
Kolisnyk, Y.
publishDate 2011
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description In this paper we obtain some results of harmonic analysis on quantum complex hyperbolic spaces. We introduce a quantum analog for the Laplace-Beltrami operator and its radial part. The latter appear to be second order q-difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/147404
citation_txt Harmonic Analysis on Quantum Complex Hyperbolic Spaces / O. Bershtein, Y. Kolisnyk // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 21 назв. — англ.
work_keys_str_mv AT bershteino harmonicanalysisonquantumcomplexhyperbolicspaces
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first_indexed 2025-12-07T20:09:48Z
last_indexed 2025-12-07T20:09:48Z
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