THE BEREZIN TRANSFORM AND ITS APPLICATIONS

doi:10.1007/s10473-021-0603-5

Abstract

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

CLC Number:

30H10

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

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THE BEREZIN TRANSFORM AND ITS APPLICATIONS

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