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Hilbert–Schimdt and Trace Class Pseudo-Differential Operators and Weyl Transforms on the Affine Group

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Abstract

We give necessary and sufficient conditions on the symbols for which the corresponding pseudo-differential operators on the affine group are Hilbert–Schimdt operators. We also give a characterization of trace class pseudo-differential operators on the affine group. A trace formula for these trace class operators is also obtained. We have also obtained the \(L^2\) boundedness of the Weyl transforms on the affine group.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, 110016, New Delhi, India

    Aparajita Dasgupta & Santosh Kumar Nayak

  2. Department of Mathematics and Statistics, York University, 4700 Keele Street, Onario, M3J 1P3, Toronto, Canada

    M. W. Wong

Authors
  1. Aparajita Dasgupta
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  2. Santosh Kumar Nayak
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  3. M. W. Wong
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Correspondence to M. W. Wong.

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The research of M. W. Wong has been supported by the Natural Sciences and Engineering Research Council of Canada under Discovery Grant 0008562. The research of Aparajita Dasgupta has been supported by Science and Engineering Research Board (SERB) under the MATRICS Grant, MTR 2019/001426.

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Dasgupta, A., Nayak, S.K. & Wong, M.W. Hilbert–Schimdt and Trace Class Pseudo-Differential Operators and Weyl Transforms on the Affine Group. J. Pseudo-Differ. Oper. Appl. 12, 11 (2021). https://doi.org/10.1007/s11868-021-00380-4

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  • DOI: https://doi.org/10.1007/s11868-021-00380-4

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