Toeplitz quantization and asymptotic expansions for real bounded symmetric domains
type: Item
instance of: scholarly article
title: Toeplitz quantization and asymptotic expansions for real bounded symmetric domains
zbMATH Open document ID: 1226.32010
author: Miroslav Engliš
author: Harald Upmeier
published in: Mathematische Zeitschrift
publication date: 2011-08-30T00:00:00Z
review text: This paper introduces a certain star restriction for the setting of real bounded symmetric domains. Let us recall that geometric quantizations of complex Kähler manifolds are very useful to study symmetric manifolds. In this case, the product of observables is described via the Weyl calculus and the Toeplitz-Berezin calculus. In this work, the authors ``generalise'' these notions to the framework of real symmetric manifolds. They introduce an analogue star operator, called star restriction. They prove the usual asymptotic expansion of this star restriction. Moreover, they establish an analogue of the theorem of Arazy and Orsted related to the Berezin transform.
reviewed by: Angela Gammella-Mathieu
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 46E22
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 53D55
zbMATH DE Number: 5944196
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: star product
zbMATH Keywords: covariant quantization
MaRDI profile type: Publication
full work available at URL: s00209-010-0702-9
OpenAlex ID: W1999369370
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DOI: 10.1007/S00209-010-0702-9
description: scientific article; zbMATH DE number 5944196