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Harmonic Analysis on Quantum Complex Hyperbolic Spaces
Symmetry, integrability and geometry: methods and applications, Tome 7 (2011) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Olga Bershtein; Yevgen Kolisnyk. Harmonic Analysis on Quantum Complex Hyperbolic Spaces. Symmetry, integrability and geometry: methods and applications, Tome 7 (2011). http://geodesic.mathdoc.fr/item/SIGMA_2011_7_a77/

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