Harmonic Analysis on Quantum Complex Hyperbolic Spaces
Quantum Algebra
2011-09-15 v3 Functional Analysis
Representation Theory
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 -difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it.
Cite
@article{arxiv.1108.3357,
title = {Harmonic Analysis on Quantum Complex Hyperbolic Spaces},
author = {Olga Bershtein and Yevgen Kolisnyk},
journal= {arXiv preprint arXiv:1108.3357},
year = {2011}
}