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

H. Mejjaoli; S. Ben Saïd

doi:10.1007/s10476-021-0091-9

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

H. Mejjaoli, S. Ben Saïd

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	629-663
Number of pages	35
Journal	Analysis Mathematica
Volume	47
Issue number	3
DOIs	https://doi.org/10.1007/s10476-021-0091-9
Publication status	Published - Sept 2021

Keywords

k-Hankel Gabor transform
k-Hankel transform
localization operator
spectrogram

ASJC Scopus subject areas

Analysis
Mathematics(all)

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10.1007/s10476-021-0091-9

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title = "k-Hankel Gabor Transform and Its Applications to the Theory of Localization Operators",

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.",

keywords = "k-Hankel Gabor transform, k-Hankel transform, localization operator, spectrogram",

author = "H. Mejjaoli and {Ben Sa{\"i}d}, S.",

note = "Funding Information: 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. Trim{\`e}che and M. W. Wong for their help. Publisher Copyright: {\textcopyright} 2021, Akad{\'e}miai Kiad{\'o}, Budapest.",

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T1 - k-Hankel Gabor Transform and Its Applications to the Theory of Localization Operators

AU - Mejjaoli, H.

AU - Ben Saïd, S.

N1 - Funding Information: 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. Publisher Copyright: © 2021, Akadémiai Kiadó, Budapest.

PY - 2021/9

Y1 - 2021/9

N2 - 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.

AB - 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.

KW - k-Hankel Gabor transform

KW - k-Hankel transform

KW - localization operator

KW - spectrogram

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JO - Analysis Mathematica

JF - Analysis Mathematica

IS - 3

ER -

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

Abstract

Keywords

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