On Function Theory in Quantum Disc: Integral Representations
arXiv:math/9808015
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 . 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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