9 citations · 24 across the 9 of their papers we have counts for
12 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…
Algebras of Toeplitz operators on the -dimensional unit ball
Wolfram Bauer, Raffael Hagger, Nikolai Vasilevski
We study -algebras generated by Toeplitz operators acting on the standard weighted Bergman space over the unit ball in $\mathbb{…
Toeplitz operators in polyanalytic Bergman type spaces
Grigori Rozenblum, Nikolai Vasilevski
We consider Toeplitz operators in Bergman and Fock type spaces of polyanalytic functions on the disk or on the half-plane with respect to the Lebesgue measure (resp.…
Uniform Continuity and Quantization on Bounded Symmetric Domains
Wolfram Bauer, Raffael Hagger, Nikolai Vasilevski
We consider Toeplitz operators with symbol acting on the standard weighted Bergman spaces over a bounded symmetric domain . Here is…
Toeplitz operators defined by sesquilinear forms: Bergman space case
Grigori Rozenblum, Nikolai Vasilevski
The definition of Toeplitz operators in the Bergman space of square integrable analytic functions in the unit disk in the complex plane is extended in such way that it cov…
Toeplitz operators in the Herglotz space
Grigori Rozenblum, Nikolai Vasilevski
We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in . As the most traditional definition of Toeplitz operators via Bergman-t…
Toeplitz operators defined by sesquilinear forms: Fock space case
Grigori Rozenblum, Nikolai Vasilevski
The classical theory of Toeplitz operators in spaces of analytic functions deals usually with symbols that are bounded measurable functions on the domain in question. A further ext…