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TOEPLITZ QUANTIZATION AND ASYMPTOTIC EXPANSIONS FOR REAL BOUNDED SYMMETRIC DOMAINS

By Miroslav Englis and Harald Upmeier

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 complexification 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 ├śrsted concerning the analogous expansion for the Berezin transform

Topics: Key words and phrases. bounded symmetric domain, Toeplitz operator, star product, covariant quantization
Year: 2010
OAI identifier: oai:CiteSeerX.psu:10.1.1.173.2540
Provided by: CiteSeerX
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