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The gyrator transform of the generalized functions

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Abstract

The gyrator transform is an integral transform that has attracted much attention in the field of optics and other engineering fields. We consider the image of the gyrator transform of the Gelfand-Shilov space and its dual space. While the gyrator transform is closely related to the fractional Fourier transform, we discuss the difference between these two transforms. Moreover, we show the relation between the above spaces and the eigenfunctions of the gyrator transform.

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Acknowledgements

The authors are thankful to the referees for multiple suggestions that helped to improve this paper.

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Author notes

  1. Toshinao Kagawa and Toshio Suzuki have authors contributed equally to this work.

Authors and Affiliations

  1. School of General and Management Studies, Suwa University of Science, 5000-1, Toyohira, Chino-shi, Nagano, 391-0292, Japan

    Toshinao Kagawa

  2. Department of Applied Mathematics, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

    Toshio Suzuki

Authors
  1. Toshinao Kagawa
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  2. Toshio Suzuki
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Correspondence to Toshio Suzuki.

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Kagawa, T., Suzuki, T. The gyrator transform of the generalized functions. J. Pseudo-Differ. Oper. Appl. 15, 37 (2024). https://doi.org/10.1007/s11868-024-00607-0

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  • DOI: https://doi.org/10.1007/s11868-024-00607-0

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