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 |
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| Date: | 2011 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147404 |
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| 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 |
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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 |
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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.
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| 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 AT kolisnyky harmonicanalysisonquantumcomplexhyperbolicspaces |
| first_indexed |
2025-12-07T20:09:48Z |
| last_indexed |
2025-12-07T20:09:48Z |
| _version_ |
1850881541211684864 |