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Mathematische Zeitschrift

, Volume 268, Issue 3–4, pp 931–967 | Cite as

Toeplitz quantization and asymptotic expansions for real bounded symmetric domains

  • Miroslav Engliš
  • Harald UpmeierEmail author
Article

Abstract

An analogue of the star product, familiar from deformation quantization, is studied in the setting of real bounded symmetric domains. The analogue turns out to be a certain invariant operator, which one might call star restriction, from functions on the hermitification of the domain into functions on the domain itself. In particular, we establish the usual (i.e. semiclassical) asymptotic expansion of this star restriction, and further obtain a real- variable analogue of a theorem of Arazy and Ørsted concerning the analogous expansion for the Berezin transform.

Keywords

Bounded symmetric domain Toeplitz operator Star product Covariant quantization 

Mathematics Subject Classification (2000)

Primary 32M15 Secondary 46E22 47B35 53D55 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Mathematics InstituteSilesian University at OpavaOpavaCzech Republic
  2. 2.Mathematics InstitutePrague 1Czech Republic
  3. 3.Fachbereich MathematikUniversität MarburgMarburgGermany

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