On Function Theory in Quantum Disc: Integral Representations

Details On Function Theory in Quantum Disc: Integral Representations On Function Theory in Quantum Disc: Integral Representations

1998-08-04

arxiv.org/abs/math/9808015v2

Mathematics

Quantum Algebra

LaTeX 2.09, 17 pages, vaksman@ilt.kharkov.ua, sinelshchikov@ilt.kharkov.ua

Scientific paper

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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