On Function Theory in Quantum Disc: Integral Representations

1998/08/04 by D. Shklyarov, Shklyarov, D., S. Sinel'shchikov +3
Mathematics · Physics and Astronomy · #81R50 (Primary) 81Q99 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.CV #math.FA #math.QA #msc:81Q99 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/9808015

LaTeX 2.09, 17 pages, [email protected], [email protected]

arxiv created 1999/09/16 · arxiv updated 2009/11/30

Abstract

The present work considers one of the simplest homogeneous spaces of the quantum group SU(1,1), the q-analogue of the unit disc in \Bbb C. We state without proofs q-analogues of Cauchy-Green formulae, integral representations of eigenfunctions of the Laplace-Beltrami operator, Green functions for Poisson equation and an inversion formula for Fourier transform. It is also demonstrated that the two-parameter quantization of the disc introduced before by S. Klimec and A. Lesniewski, can be derived via an application of the method of F. Berezin.

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