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

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-frequ...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2021-09, Vol.47 (3), p.629-663
Main Authors: Mejjaoli, H., Ben Saïd, S.
Format: Article
Language:English
Subjects:
Analysis
Eigenvalues
Eigenvectors
Gabor transformation
Localization
Mathematics
Mathematics and Statistics
Operators
Spectrograms
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Summary: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.
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-021-0091-9