12 papers · 1 filter
q-Analogues for Green functions for powers of the invariant Laplacian in the unit disc
D. Shklyarov
In a recent work of J. Peetre and M. Englius explicit formulae were obtained for Green functions of the powers of the Möbius-invariant Laplace operator in the unit disc. In the pre…
Quantum matrix ball: the Bergman kernel
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
In our preprint q-alg/9703005 q-analogues of bounded symmetric domains were defined to be homogeneous spaces of the associated quantum groups. The investigation of a simplest among…
Quantum matrix ball: differential and integral calculi
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
We have introduced q-analogues of bounded symmetric domains in our work q-alg/9703005. Given the simplest ones among those, the works q-alg/9603012 and math.QA/9803110 announce the…
q-Analogue of the Berezin quantization method
D. Shklyarov, S. Sinel'shchikov, L. Vaksman
We use Berezin's quantization procedure to obtain a formal -invariant deformation of the quantum disc. Explicit formulae for the associated q-bidifferential operators…
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…