THE BEREZIN TRANSFORM AND ITS APPLICATIONS

doi:10.1007/s10473-021-0603-5

摘要/Abstract

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

Kehe ZHU. THE BEREZIN TRANSFORM AND ITS APPLICATIONS[J]. 数学物理学报(英文版), 2021, 41(6): 1839-1858.

Kehe ZHU. THE BEREZIN TRANSFORM AND ITS APPLICATIONS[J]. Acta mathematica scientia,Series B, 2021, 41(6): 1839-1858.

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