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An Excursion into Berezin–Toeplitz Quantization and Related Topics

  • Miroslav EnglišEmail author
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 251)

Abstract

We present an introduction to the Berezin and Berezin–Toeplitz quantizations, starting from their historical origins and relationships with other quantization methods, discussing various instructive examples like the Segal–Bargmann–Fock space, and culminating by highlights of proofs of the existence of these quantizations using both the Boutet de Monvel theory and the approach via Fefferman’s expansion and Forelli–Rudin construction. The exposition strives to be reasonably self-contained and accessible to nonexperts.

Keywords

Berezin quantization Toeplitz operator Bergman space Bergman kernel Berezin transform 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Mathematics InstituteSilesian University in OpavaOpavaCzech Republic
  2. 2.Mathematics InstitutePrague 1Czech Republic

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