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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Asymptotic expansions for Toeplitz operators on symmetric spaces of general type


Authors: Miroslav Engliš and Harald Upmeier
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 32M15; Secondary 46E22, 47B35, 53D55
Published electronically: March 31, 2014
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Abstract: A general theory of Berezin-Toeplitz quantization for symmetric spaces is presented, with emphasis on representation-theoretic asymptotic expansions, which applies to spaces of compact and non-compact type, both in the classical setting of hermitian symmetric spaces and also for their real forms. The Berezin (or Wick type) calculus and its opposite ``anti-Wick'' type calculus are treated on an equal footing.


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Additional Information

Miroslav Engliš
Affiliation: Mathematics Institute, Silesian University at Opava, Na Rybníčku 1, 74601 Opava, Czech Republic — and — Mathematics Institute, Žitná 25, 11567 Prague 1, Czech Republic
Email: englis{@}math.cas.cz

Harald Upmeier
Affiliation: Fachbereich Mathematik, Universität Marburg, D-35032 Marburg, Germany
Email: upmeier{@}mathematik.uni-marburg.de

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06130-8
PII: S 0002-9947(2014)06130-8
Keywords: Symmetric space, symmetric domain, Berezin quantization, Toeplitz quantization, Berezin transform
Received by editor(s): April 27, 2012
Received by editor(s) in revised form: March 9, 2013
Published electronically: March 31, 2014
Additional Notes: The first author’s research was supported by GAČR grant no. 201/09/0473 and AV ČR institutional research plan AV0Z10190503.
The second author’s research was supported by GIF grant no. 696-17.6/2001
Article copyright: © Copyright 2014 American Mathematical Society