Harmonic Analysis on Quantum Complex Hyperbolic Spaces

Details Harmonic Analysis on Quantum Complex Hyperbolic Spaces Harmonic Analysis on Quantum Complex Hyperbolic Spaces

2011-08-16

arxiv.org/abs/1108.3357v3

SIGMA 7 (2011), 078, 19 pages

Mathematics

Quantum Algebra

Scientific paper

10.3842/SIGMA.2011.078

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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