The Berezin transform and operators on spaces of analytic functions

Karel Stroethoff

Banach Center Publications (1997)

  • Volume: 38, Issue: 1, page 361-380
  • ISSN: 0137-6934

Abstract

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In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz operators 6. Sarason's example

How to cite

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Stroethoff, Karel. "The Berezin transform and operators on spaces of analytic functions." Banach Center Publications 38.1 (1997): 361-380. <http://eudml.org/doc/208641>.

@article{Stroethoff1997,
abstract = {In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz operators 6. Sarason's example},
author = {Stroethoff, Karel},
journal = {Banach Center Publications},
keywords = {commutativity of Toeplitz operators; Berezin transform; symbol; spaces of analytic functions; Hardy space; Bergman space; Fock space},
language = {eng},
number = {1},
pages = {361-380},
title = {The Berezin transform and operators on spaces of analytic functions},
url = {http://eudml.org/doc/208641},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Stroethoff, Karel
TI - The Berezin transform and operators on spaces of analytic functions
JO - Banach Center Publications
PY - 1997
VL - 38
IS - 1
SP - 361
EP - 380
AB - In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz operators 6. Sarason's example
LA - eng
KW - commutativity of Toeplitz operators; Berezin transform; symbol; spaces of analytic functions; Hardy space; Bergman space; Fock space
UR - http://eudml.org/doc/208641
ER -

References

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