Harmonic Analysis on Quantum Complex Hyperbolic Spaces

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.

References in corpus (4)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• On Function Theory in Quantum Disc: q-Differential Equations and Fourier Transform
• Plancherel formula for the quantum matrix ball - I
• Function Theory on a q-Analog of Complex Hyperbolic Space

Cited by in corpus (1)

• Noncommutative Harmonic Analysis on Quantum Hyperbolic Spaces. The Laplace-Beltrami Operator