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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
References:
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
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Document Type: Article
Language: English
Citation: Olga Bershtein, Yevgen Kolisnyk, “Harmonic Analysis on Quantum Complex Hyperbolic Spaces”, SIGMA, 7 (2011), 078, 19 pp.
Citation in format AMSBIB
\Bibitem{BerKol11}
\by Olga Bershtein, Yevgen Kolisnyk
\paper Harmonic Analysis on Quantum Complex Hyperbolic Spaces
\jour SIGMA
\yr 2011
\vol 7
\papernumber 078
\totalpages 19
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\crossref{https://doi.org/10.3842/SIGMA.2011.078}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84896061615}
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