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k-Hankel Gabor Transform and Its Applications to the Theory of Localization Operators

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Abstract

We introduce and study the k-Hankel Gabor transform. We investigate the localization operators for this transform. In particular, we study their trace class properties and we prove that they belong to the Schatten-von Neumann class. We also study the eigenvalues and eigenfunctions of the time-frequency localization operator. Finally we give some results on the spectrograms for the k-Hankel Gabor transform.

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Acknowledgements

The authors are deeply indebted to the referees for providing constructive comments and helps in improving the contents of this article. The first author thanks professors K. Trimèche and M. W. Wong for their help.

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Authors and Affiliations

  1. College of Sciences, Department of Mathematics, Taibah University, PO Box 30002, Al Madinah Al Munawarah, Saudi Arabia

    H. Mejjaoli

  2. Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain Abu Dhabi, UAE

    S. Ben Saïd

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  1. H. Mejjaoli
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  2. S. Ben Saïd
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Correspondence to H. Mejjaoli.

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Mejjaoli, H., Ben Saïd, S. k-Hankel Gabor Transform and Its Applications to the Theory of Localization Operators. Anal Math 47, 629–663 (2021). https://doi.org/10.1007/s10476-021-0091-9

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  • DOI: https://doi.org/10.1007/s10476-021-0091-9

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