Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (6): 1839-1858.doi: 10.1007/s10473-021-0603-5

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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).

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