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Toeplitz quantization and asymptotic expansions for real bounded symmetric domains

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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.

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Authors and Affiliations

  1. Mathematics Institute, Silesian University at Opava, Na Rybníčku 1, 74601, Opava, Czech Republic

    Miroslav Engliš

  2. Mathematics Institute, Žitná 25, 11567, Prague 1, Czech Republic

    Miroslav Engliš

  3. Fachbereich Mathematik, Universität Marburg, 35032, Marburg, Germany

    Harald Upmeier

Authors
  1. Miroslav Engliš
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  2. Harald Upmeier
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Correspondence to Harald Upmeier.

Additional information

Research supported by GA ČR Grant no. 201/06/0128, AV ČR institutional research plan AV0Z10190503 and GIF Grant no. 696-17.6/2001.

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Engliš, M., Upmeier, H. Toeplitz quantization and asymptotic expansions for real bounded symmetric domains. Math. Z. 268, 931–967 (2011). https://doi.org/10.1007/s00209-010-0702-9

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  • DOI: https://doi.org/10.1007/s00209-010-0702-9

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