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Harmonic Analysis on Quantum Complex Hyperbolic Spaces
Olga Bershtein, Yevgen Kolisnyk Institute for Low Temperature Physics and Engineering, 47 Lenin Ave., 61103, Kharkov, Ukraine
Abstract:
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.
Keywords:
quantum groups, harmonic analysis on quantum symmetric spaces; $q$-difference operators;
Al-Salam–Chihara polynomials; Plancherel formula.
Received: April 30, 2011; in final form August 10, 2011; Published online August 18, 2011
Citation:
Olga Bershtein, Yevgen Kolisnyk, “Harmonic Analysis on Quantum Complex Hyperbolic Spaces”, SIGMA, 7 (2011), 078, 19 pp.
Linking options:
https://www.mathnet.ru/eng/sigma636 https://www.mathnet.ru/eng/sigma/v7/p78
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Abstract page: | 262 | Full-text PDF : | 49 | References: | 47 |
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