%0 Journal Article
%T Harmonic Analysis on Quantum Complex Hyperbolic Spaces
%A Olga Bershtein
%A Yevgen Kolisnyk
%J Mathematics
%D 2011
%I arXiv
%R 10.3842/SIGMA.2011.078
%X 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.
%U http://arxiv.org/abs/1108.3357v3