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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Asymptotic expansions for Toeplitz operators on symmetric spaces of general type
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by Miroslav Engliš and Harald Upmeier PDF
Trans. Amer. Math. Soc. 367 (2015), 423-476 Request permission

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
  • 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
  • © Copyright 2014 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 423-476
  • MSC (2010): Primary 32M15; Secondary 46E22, 47B35, 53D55
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06130-8
  • MathSciNet review: 3271267