Quantitative Uncertainty Principles Associated with the k-Generalized Stockwell Transform

Mejjaoli, Hatem; Trimèche, Khalifa

doi:10.1007/s00009-021-01968-2

Cited by 5 publications

(3 citation statements)

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“…The aim of this section is to present a healthy overview of the prerequisites circumscribing the Riemann-Liouville operator, Schatten-von Neumann classes, and the generalized Stockwell transform. For a detailed perspective regarding the content of the section, we refer to [4,9,27,36,38]. For the sake of distinction, we sub-divide the section into three subsections.…”

Section: Preliminariesmentioning

confidence: 99%

“…In this subsection, we shall recall some fundamental results on the generalized Stockwell transforms due to Ben Hamadi, Ghandouri and Hafirassou (see [9]) and Mejjaoli [27].…”

Section: Basic Generalized Stockwell Theorymentioning

confidence: 99%

“…In this paper, we continue the study of some problems of harmonic analysis associated with the generalized Stockwell transform started in [9,27]. Particularly, motivated by Wong's approaches, the aim of the first part of this paper is to study the boundedness and compactness of localization operators associated with generalized Stockwell transforms.…”

Section: Introductionmentioning

confidence: 99%

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Time-frequency analysis associated with the generalized Stockwell transform

Ben Hamadi,

Hafirassou,

Mejjaolı

2024

Hacettepe Journal of Mathematics and Statistics

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The Riemann-Liouville operator has been extensively investigated and has witnessed a remarkable development in numerous fields of harmonic analysis. In this paper, we consider the Stockwell transform associated with the Riemann-Liouville operator. Knowing the fact that the study of the time-frequency analysis are both theoretically interesting and practically useful, we investigated several problems for this subject on the setting of this generalized Stockwell transform. Firstly, we explore the Shapiro uncertainty principle for this transform. Next, we study the boundedness and compactness of localization operators associated with the generalized Stockwell transforms. Finally, the scalogram for the generalized Stockwell transform are introduced and studied at the end.

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Section: Preliminariesmentioning

confidence: 99%

“…In this subsection, we shall recall some fundamental results on the generalized Stockwell transforms due to Ben Hamadi, Ghandouri and Hafirassou (see [9]) and Mejjaoli [27].…”

Section: Basic Generalized Stockwell Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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