2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77245The 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.LaTeX 2.09, 17 pages, vaksman@ilt.kharkov.ua, sinelshchikov@ilt.kharkov.uaQuantum AlgebraHigh Energy Physics - TheoryComplex VariablesFunctional Analysis81R50 (Primary) 81Q99 (Secondary)text