10 papers
Spectral theorem approach to commutative C* -algebras generated by Toeplitz operators on the unit ball: quasi-elliptic related cases
Grigori Rozenblum, Nikolai Vasilevski
We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in . For the algebras of elliptic type we find a…
Commutative algebras of Toeplitz operators on the Bergman space revisited: Spectral theorem approach
Grigori Rozenblum, Nikolai Vasilevski
For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the alge…
Poly-analytic functions AND representation theory
Alexander V Turbiner, Nikolai L Vasilevski
We propose the Lie-algebraic interpretation of poly-analytic functions in $L_2(\C,dμ)$, with the Gaussian measure , based on a flag structure formed by the representation space…
Trace class Toeplitz operators with singular symbols
Grigori Rozenblum, Nikolai Vasilevski
We characterize the trace class membership of Toeplitz operators with distributional symbols acting on the Bergman space on the unit disk. The Berezin transform of distributions, i…
Toeplitz operators with singular symbols in polyanalytic Bergman spaces on the half-plane
Grigori Rozenblum, Nikolai Vasilevski
Using the approach based on sesquilinear forms, we introduce Toeplitz operator in the analytic Bergman space on the upper half-plane with strongly singular symbols, derivatives of…
-invariant Fock-Carleson type measures for derivatives of order and the corresponding Toeplitz operators
Kevin Esmeral, Grigori Rozenblum, Nikolai Vasilevski
Our purpose is to characterize the so-called horizontal Fock-Carleson type measures for derivatives of order (we write it -hFC for short) for the Fock space as well as the T…