Generalized Stockwell transforms: Spherical mean operators and applications
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Saifallah Ghobber
und
Hatem Mejjaoli
Abstract
The spherical mean operator has been widely studied and has seen remarkable development in many areas of harmonic analysis. In this paper, we consider the Stockwell transform related to the spherical mean operator. Since the study of time-frequency analysis is both theoretically interesting and practically useful, we will study several problems for the generalized Stockwell transform. Firstly, we explore the Shapiro uncertainty principle for this transformation. Next, we will study the boundedness and then the compactness of localization operators related to the generalized Stockwell transform, and finally we will introduce and study its scalogram.
Acknowledgements
The second author dedicated this paper to Professor Mohamed Selmi for his support and help, and for his distinguished career in mathematics, and especially for his contribution to the Tunisian School in Potential theory. The authors are deeply indebted to the referees for providing constructive comments which improved the contents of this article.
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Fractional p-Laplacian elliptic Dirichlet problems
- Group invertibility of the sum in rings and its applications
- σ-symmetric amenability of Banach algebras
- Generalized Stockwell transforms: Spherical mean operators and applications
- Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions
- Capacity in Besov and Triebel–Lizorkin spaces with generalized smoothness
- Existence of solutions for (p(y),q(y))-Laplacian elliptic problem on an exterior domain
- Degeneration phenomenon in linear ordinary differential equations
- Weak type estimates of genuine Calderón–Zygmund operators on the local Morrey spaces associated with ball quasi-Banach function spaces
- Generalized derivation on semiprime and prime Banach algebras
- Weak positive solutions to singular quasilinear elliptic equation
- Constructions and characterizations of mixed reverse-order laws for the Moore–Penrose inverse and group inverse
- Integral inequalities of Ostrowski type for two kinds of s-logarithmically convex functions
- On the polar dualities and star dualities of the quasi Lp -intersection bodies
- New estimates for the Berezin number of Hilbert space operators
- Addendum to On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology
Artikel in diesem Heft
- Frontmatter
- Fractional p-Laplacian elliptic Dirichlet problems
- Group invertibility of the sum in rings and its applications
- σ-symmetric amenability of Banach algebras
- Generalized Stockwell transforms: Spherical mean operators and applications
- Existence of positive weak solutions for stationary fractional Laplacian problem by using sub-super solutions
- Capacity in Besov and Triebel–Lizorkin spaces with generalized smoothness
- Existence of solutions for (p(y),q(y))-Laplacian elliptic problem on an exterior domain
- Degeneration phenomenon in linear ordinary differential equations
- Weak type estimates of genuine Calderón–Zygmund operators on the local Morrey spaces associated with ball quasi-Banach function spaces
- Generalized derivation on semiprime and prime Banach algebras
- Weak positive solutions to singular quasilinear elliptic equation
- Constructions and characterizations of mixed reverse-order laws for the Moore–Penrose inverse and group inverse
- Integral inequalities of Ostrowski type for two kinds of s-logarithmically convex functions
- On the polar dualities and star dualities of the quasi Lp -intersection bodies
- New estimates for the Berezin number of Hilbert space operators
- Addendum to On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology
