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arXiv · 1108.3357

Harmonic Analysis on Quantum Complex Hyperbolic Spaces

Olga Bershtein·Yevgen Kolisnyk
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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.

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BibTeXRIS

Olga Bershtein, Yevgen Kolisnyk. 2011-09-14. Harmonic Analysis on Quantum Complex Hyperbolic Spaces. https://doi.org/10.3842/sigma.2011.078

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