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Map** properties for the Bargmann transform on modulation spaces

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Abstract

We investigate map** properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions. We also present some consequences. For example we prove that the spectrum of the Harmonic oscillator is the same for all modulation spaces.

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Author notes

  1. Joachim Toft

    Present address: Department of Computer Science, Physics and Mathematics, Linnæus University, Växjö, Sweden

Authors and Affiliations

  1. Department of Mathematics, University of Agder, Kristiansand, Norway

    Mikael Signahl

  2. Department of Mathematics and Systems Engineering, Växjö University, Växjö, Sweden

    Joachim Toft

Authors
  1. Mikael Signahl
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  2. Joachim Toft
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Correspondence to Joachim Toft.

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Signahl, M., Toft, J. Map** properties for the Bargmann transform on modulation spaces. J. Pseudo-Differ. Oper. Appl. 3, 1–30 (2012). https://doi.org/10.1007/s11868-011-0039-0

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  • DOI: https://doi.org/10.1007/s11868-011-0039-0

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