On Function Theory in Quantum Disc: Integral Representations
Quantum Algebra
2007-05-23 v2 High Energy Physics - Theory
Complex Variables
Functional Analysis
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.
Keywords
Cite
@article{arxiv.math/9808015,
title = {On Function Theory in Quantum Disc: Integral Representations},
author = {D. Shklyarov and S. Sinel'shchikov and L. Vaksman},
journal= {arXiv preprint arXiv:math/9808015},
year = {2007}
}
Comments
LaTeX 2.09, 17 pages, [email protected], [email protected]