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Harmonic Analysis on Quantum Complex Hyperbolic Spaces
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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Harmonic Analysis on Quantum Complex Hyperbolic Spaces
Інший ID:
2010 Mathematics Subject Classification: 17B37; 20G42; 81R50; 33D45; 42C10
DOI: http://dx.doi.org/10.3842/SIGMA.2011.078
DOI: http://dx.doi.org/10.3842/SIGMA.2011.078
Посилання:
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.
Підтримка:
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.
Дата:
2011
Переглядів:
511
Завантажень:
301
Анотація:
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.
