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On the Weinstein–Wigner transform and Weinstein–Weyl transform

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In this paper, we define and study the Weinstein–Wigner transform and we prove its inversion formula. Next, we introduce and study the Weinstein–Weyl transform \({\mathcal {W}}_\sigma \) with symbol \(\sigma \) and we give an integral relation between it and the Weinstein–Wigner transform. At last, we give criteria in terms of \(\sigma \) for boundedness and compactness of the transform \({\mathcal {W}}_\sigma \).

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Correspondence to Ahmed Saoudi.

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Saoudi, A. On the Weinstein–Wigner transform and Weinstein–Weyl transform. J. Pseudo-Differ. Oper. Appl. 11, 1–14 (2020). https://doi.org/10.1007/s11868-019-00313-2

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  • Weinstein–Wigner transform
  • Weinstein–Weyl transform
  • Inversion formula
  • Boundedness and compactness