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Dual of 2D Fractional Fourier Transform Associated to Itô–Hermite Polynomials

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Abstract

A class of integral transforms, on the planar Gaussian Hilbert space with range in the weighted Bergman space on the bi-disk, is defined as the dual transforms of the 2d fractional Fourier transform associated with the Mehler function for Itô–Hermite polynomials. Some spectral properties of these transforms are investigated. Namely, we study their boundedness and identify their null spaces as well as their ranges. Such identification depends on the zeros set of Itô–Hermite polynomials. Moreover, the explicit expressions of their singular values are given and compactness and membership in p-Schatten class are studied. The relationship to specific fractional Hankel transforms is also established.

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Authors and Affiliations

  1. Analysis, P.D.E. and Spectral Geometry, Lab M.I.A.-S.I., CeReMAR, Department of Mathematics, Faculty of Sciences, Mohammed V University in Rabat, P.O. Box 1014, Rabat, Morocco

    Abdelhadi Benahmadi & Allal Ghanmi

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  1. Abdelhadi Benahmadi
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  2. Allal Ghanmi
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Correspondence to Abdelhadi Benahmadi.

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Dedicated to the memory of Professor Elhachmia Ait Benhaddou.

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Benahmadi, A., Ghanmi, A. Dual of 2D Fractional Fourier Transform Associated to Itô–Hermite Polynomials. Results Math 75, 168 (2020). https://doi.org/10.1007/s00025-020-01297-y

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