5 citations · 13 across the 11 of their papers we have counts for
12 papers
Maximum modulus principle for "holomorphic functions" on the quantum matrix ball
Olga Bershtein, Olof Giselsson, Lyudmila Turowska
We describe the Shilov boundary ideal for a q-analog of the algebra of holomorphic functions on the unit ball in the space of matrices and show that its -envelope…
Noncommutative Harmonic Analysis on Quantum Hyperbolic Spaces. The Laplace-Beltrami Operator
Olga Bershtein
In this paper we study the Laplace-Beltrami operator on quantum complex hyperbolic spaces. We describe its action in terms of certain -difference operators of second order and p…
On *-representations of polynomial algebras in quantum matrix spaces of rank 2
Olga Bershtein
In this paper we study of *-representations for polynomial algebras on quantum matrix spaces. We deal with two special cases of the polynomial algebras, namely the algebra of polyn…
Function Theory on a q-Analog of Complex Hyperbolic Space
O. Bershtein, S. D. Sinel'shchikov
This work deals with function theory on quantum complex hyperbolic spaces. The principal notions are expounded. We obtain explicit formulas for invariant integrals on `finite' func…
A q-Analog of the Hua Equations
O. Bershtein, S. Sinel'shchikov
A necessary condition is established for a function to be in the image of a quantum Poisson integral operator associated to the Shilov boundary of the quantum matrix ball. A quantu…
Plancherel formula for the quantum matrix ball - I
O. Bershtein, Ye. Kolisnyk
Plancherel formula is one of the celebrated result of harmonic analysis on semisimple Lie groups and their homogeneous spaces. The main goal of this work is to find a q-analog of t…