THE BEREZIN TRANSFORM AND COMMUTATIVITY OFTOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THEUPPER HALF-PLANE

The aim of this paper is twofold.First, we explore the role of the pioneering concept of the Berezin transform and its fixed points in the framework of the Bergman space on the complex upper half-plane.Second, in the setting of this Bergman space, we characterize commuting pairs of Toeplitz operators with bounded symbols that are either harmonic, of bi-harmonic type, or of bi-analytic type.In particular, this allows us to characterize normal Toeplitz operators.

Publication Details

Journal
Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan
Published
2025-01-01
DOI
https://doi.org/10.30546/2409-4994.2025.51.1.1029
Primary Topic
Holomorphic and Operator Theory
Type
article
Field-Weighted Citation Impact
0.00
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article

THE BEREZIN TRANSFORM AND COMMUTATIVITY OFTOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THEUPPER HALF-PLANE

Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan
Holomorphic and Operator Theory
article

THE BEREZIN TRANSFORM AND COMMUTATIVITY OFTOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THEUPPER HALF-PLANE

article en

Abstract

The aim of this paper is twofold.First, we explore the role of the pioneering concept of the Berezin transform and its fixed points in the framework of the Bergman space on the complex upper half-plane.Second, in the setting of this Bergman space, we characterize commuting pairs of Toeplitz operators with bounded symbols that are either harmonic, of bi-harmonic type, or of bi-analytic type.In particular, this allows us to characterize normal Toeplitz operators.

Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan
Openalex Percentile: Top 83%
Holomorphic and Operator Theory
DOIOpen Access PDFOpenAlex
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THE BEREZIN TRANSFORM AND COMMUTATIVITY OFTOEPLITZ OPERATORS ON THE BERGMAN SPACE OF THEUPPER HALF-PLANE · Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan (2025) | TGRS Research Map | TGRS