Harmonic analysis problems associated with the k-Hankel Gabor transform

Hatem Mejjaoli; Salem Ben Saïd

doi:10.1007/s11868-020-00356-w

Harmonic analysis problems associated with the k-Hankel Gabor transform

Hatem Mejjaoli
, Salem Ben Saïd

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

We introduce a continuous k-Hankel Gabor transform acting on a Hilbert space deforming L²(R). We prove a Plancherel formula and L²-inversion formulas for it. We also prove several uncertainty principles for this transform such as Heisenberg type inequalities and Faris–Price type uncertainty principle.

Original language	English
Pages (from-to)	1549-1593
Number of pages	45
Journal	Journal of Pseudo-Differential Operators and Applications
Volume	11
Issue number	4
DOIs	https://doi.org/10.1007/s11868-020-00356-w
Publication status	Published - Dec 1 2020

Keywords

Faris–Price’s uncertainty principle
Heisenberg’s type inequality
Inversion theorem
Local Cowling–Price’s type inequalities
Plancherel formula
k-Hankel Gabor transform
k-Hankel transform

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s11868-020-00356-w

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title = "Harmonic analysis problems associated with the k-Hankel Gabor transform",

abstract = "We introduce a continuous k-Hankel Gabor transform acting on a Hilbert space deforming L2(R). We prove a Plancherel formula and L2-inversion formulas for it. We also prove several uncertainty principles for this transform such as Heisenberg type inequalities and Faris–Price type uncertainty principle.",

keywords = "Faris–Price{\textquoteright}s uncertainty principle, Heisenberg{\textquoteright}s type inequality, Inversion theorem, Local Cowling–Price{\textquoteright}s type inequalities, Plancherel formula, k-Hankel Gabor transform, k-Hankel transform",

author = "Hatem Mejjaoli and \{Ben Sa{\"i}d\}, Salem",

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year = "2020",

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AU - Ben Saïd, Salem

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N2 - We introduce a continuous k-Hankel Gabor transform acting on a Hilbert space deforming L2(R). We prove a Plancherel formula and L2-inversion formulas for it. We also prove several uncertainty principles for this transform such as Heisenberg type inequalities and Faris–Price type uncertainty principle.

AB - We introduce a continuous k-Hankel Gabor transform acting on a Hilbert space deforming L2(R). We prove a Plancherel formula and L2-inversion formulas for it. We also prove several uncertainty principles for this transform such as Heisenberg type inequalities and Faris–Price type uncertainty principle.

KW - Faris–Price’s uncertainty principle

KW - Heisenberg’s type inequality

KW - Inversion theorem

KW - Local Cowling–Price’s type inequalities

KW - Plancherel formula

KW - k-Hankel Gabor transform

KW - k-Hankel transform

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UR - https://www.scopus.com/pages/publications/85089866190#tab=citedBy

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JO - Journal of Pseudo-Differential Operators and Applications

JF - Journal of Pseudo-Differential Operators and Applications

IS - 4

ER -

Harmonic analysis problems associated with the k-Hankel Gabor transform

Abstract

Keywords

ASJC Scopus subject areas

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