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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 qq-difference operator, whose eigenfunctions are related to the Al-Salam-Chihara polynomials. We prove a Plancherel type theorem for it.

Keywords

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}
}
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