Year: 1998
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Shklyarov, D., Sinel'shchikov, S., Vaksman, L.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1491564485