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Symmetry, Integrability and Geometry: Methods and Applications, 2011, Volume 7, 078, 19 pp.
DOI: https://doi.org/10.3842/SIGMA.2011.078 (Mi sigma636) 		 
Harmonic Analysis on Quantum Complex Hyperbolic Spaces

Olga Bershtein, Yevgen Kolisnyk

Institute for Low Temperature Physics and Engineering, 47 Lenin Ave., 61103, Kharkov, Ukraine
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DOI: https://doi.org/10.3842/SIGMA.2011.078
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
Bibliographic databases:
Document Type: Article
MSC: 17B37; 20G42; 81R50; 33D45; 42C10
Language: English
Citation: Olga Bershtein, Yevgen Kolisnyk, “Harmonic Analysis on Quantum Complex Hyperbolic Spaces”, SIGMA, 7 (2011), 078, 19 pp.
Citation in format AMSBIB
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\paper Harmonic Analysis on Quantum Complex Hyperbolic Spaces
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