数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (6): 1839-1858.doi: 10.1007/s10473-021-0603-5

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THE BEREZIN TRANSFORM AND ITS APPLICATIONS

Kehe ZHU   

  1. Department of Mathematics and Statistics, State University of New York, Albany, NY 12222, USA
  • 收稿日期:2021-02-18 修回日期:2021-07-05 出版日期:2021-12-25 发布日期:2021-12-27
  • 作者简介:Kehe ZHU,E-mail:kzhu@albany.edu
  • 基金资助:
    Research partially supported by NNSF of China (11720101003), NSF of Guangdong Province (2018A030313512), Key projects of fundamental research in universities of Guangdong Province (2018KZDXM034) and STU Scientific Research Foundation (NTF17009).

THE BEREZIN TRANSFORM AND ITS APPLICATIONS

Kehe ZHU   

  1. Department of Mathematics and Statistics, State University of New York, Albany, NY 12222, USA
  • Received:2021-02-18 Revised:2021-07-05 Online:2021-12-25 Published:2021-12-27
  • Supported by:
    Research partially supported by NNSF of China (11720101003), NSF of Guangdong Province (2018A030313512), Key projects of fundamental research in universities of Guangdong Province (2018KZDXM034) and STU Scientific Research Foundation (NTF17009).

摘要: We give a survey on the Berezin transform and its applications in operator theory. The focus is on the Bergman space of the unit disk and the Fock space of the complex plane. The Berezin transform is most effective and most successful in the study of Hankel and Toepltiz operators.

关键词: reproducing kernel, reproducing kernel Hilbert space, Hardy space, Bergman space, Fock space, Berezin transform, Toeplitz operator, Hankel operator, composition operator

Abstract: We give a survey on the Berezin transform and its applications in operator theory. The focus is on the Bergman space of the unit disk and the Fock space of the complex plane. The Berezin transform is most effective and most successful in the study of Hankel and Toepltiz operators.

Key words: reproducing kernel, reproducing kernel Hilbert space, Hardy space, Bergman space, Fock space, Berezin transform, Toeplitz operator, Hankel operator, composition operator

中图分类号: 

  • 30H10