8 papers · 1 filter
On Function Theory in Quantum Disc: A q-Analogue of Berezin Transform
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
This work contains a proof of theorem 7.3 from math.QA/9808015. This theorem demonstrates the Berezin method to be applicable for producing a well known one-parameter deformation o…
Quantum matrix ball: the weighted Bergman kernels
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
We proceed with studying the q-analogues of Cartan domains introduced in q-alg/9703005 and turn to the case of a ball in the space of complex matrices. An explicit expression for a…
On Function Theory in Quantum Disc: q-Differential Equations and Fourier Transform
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
This work presents proofs of the main results of (math.QA/9808015), except those on q-Berezin transform to appear in a subsequent work. The notation and the results of (math.QA/980…
On Function Theory in Quantum Disc: Invariant Kernels
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
In our earlier work math.QA/9808015 some results on integral representations of functions in quantum disc were announced. It was then shown in math.QA/9808037 that the validity of…
On Function Theory in Quantum Disc: Covariance
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
Our previous work (math.QA/9808015) introduces the basic notions and announces some results on function theory in the quantum disc. The present paper establishes a relationship bet…
On Function Theory in Quantum Disc: Integral Representations
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
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 o…