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Laeng-Morpurgo-Type Uncertainty Inequalities for the Laguerre Transform

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Journal of Mathematical Research with Applications 2022年第1期42卷 8-14页

作者： fethi soltani Faculté des Sciences de Tunis Laboratoire d’Analyse Mathématique et Applications LR11ES11Université de Tunis El Manar Ecole Nationale d’Ingénieurs de Carthage Université de Carthage

In this work,we prove Clarkson-type and Nash-type inequalities for the Laguerre transform■ on M=[0,∞)×*** combining these inequalities,we show Laeng-Morpurgo-type uncertainty *** establish also a local-type uncertainty inequalities for the Laguerre transform ■,and we deduce a Heisenberg-Pauli-Weyl-type inequality for this transform.

关键词： Laeng-Morpurgo-type inequality local-type inequality Heisenberg-Pauli-Weyl-type inequality

Dunkl Multiplier Operators on a Class of Reproducing Kernel Hilbert Spaces

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Journal of Mathematical Research with Applications 2016年第6期36卷 689-702页

作者： fethi soltani Department of Mathematics Faculty of ScienceJazan University

We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark’s uncertainty *** these operators we give also an application of the th... 详细信息

关键词： Sobolev-Dunkl spaces Dunkl multiplier operators Heisenberg-Pauli-Weyl uncertainty principle Donoho-Stark uncertainty principle Tikhonov regularization extremal functions

Uncertainty Principles for the Segal-Bargmann Transform

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Journal of Mathematical Research with Applications 2017年第5期37卷 563-576页

作者： fethi soltani Department of Mathematics Faculty of Science Jazan University

We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles: local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark’s uncerta... 详细信息

关键词： Segal-Bargmann space Segal-Bargmann transform local uncertainty principle Heisenberg uncertainty principle Donoho-Stark’s uncertainty principle

Inversion Formula for the Dunkl-Wigner Transform and Compactness Property for the Dunkl-Weyl Transforms

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Journal of Mathematical Research with Applications 2015年第4期35卷 425-434页

作者： fethi soltani Department of Mathematics Faculty of ScienceJazan University

We define and study the Fourier-Wigner transform associated with the Dunkl operators,and we prove for this transform an inversion ***,we introduce and study the Weyl transforms W;associated with the Dunkl operators,where cr is a symbol in the Schwartz space S（R;×R;）.An integral relation between the precedent Weyl and Wigner transforms is *** last,we give criteria in terms of σ for boundedness and compactness of the transform W;.

关键词： Dunkl transform Dunkl-Wigner transform Dunkl-Weyl transforms inversion formula boundedness and compactness

Multiplication and Translation Operators on the Fock Spaces for the q-Modified Bessel Function

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Advances in Pure Mathematics 2011年第4期1卷 221-227页

作者： fethi soltani 不详

We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators o... 详细信息

关键词： Generalized q-Fock Spaces q-Iα Modified Bessel Function q-Bessel Operator Multiplication Operator q-Translation Operators

Toeplitz and Translation Operators on the q-Fock Spaces

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Advances in Pure Mathematics 2011年第6期1卷 325-333页

作者： fethi soltani 不详

In this work, we introduce a class of Hilbert spaces Fq of entire functions on the disk , , with reproducing kernel given by the q-exponential function eq(z);and we prove some properties concerning Toeplitz operators on this space. The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Dq by and the q-Derivative operator on the Fock space Fq;and we prove that these operators are adjoint-operators and continuous from this space into itself. Lastly, we study a generalized translation operators and a Weyl commutation relations on Fq .

关键词： q-Fock Spaces q-Exponential Function q-Derivative Operator q-Translation Operators q-Toeplitz Operators q-Weyl Commutation Relations

Fock Spaces for the q-Dunkl Kernel

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Advances in Pure Mathematics 2012年第3期2卷 169-176页

作者： fethi soltani Higher College of Technology and Informatics Tunis Tunisia

In this work, we introduce a class of Hilbert spaces of entire functions on the disk , 0 详细信息

In this work, we introduce a class of Hilbert spaces of entire functions on the disk , 0

关键词： Generalized q-Fock Spaces q-Dunkl Kernel q-Dunkl Operator q-Translation Operators

The Commutants of the Dunkl Operators on <i>ε</i>(R<sup>d</sup>)

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Advances in Pure Mathematics 2012年第4期2卷 274-297页

作者： Mohamed Sifi fethi soltani Department of Mathematics Faculty of Sciences of Tunis University of Tunis Tunis Tunisia Higher College of Technology and Informatics Tunis Tunisia

We consider the harmonic analysis associated with the Dunkl operators on Rd. We study the Dunkl mean-periodic functions on the space ε(Rd) (the space of C∞-functions). We characterize also the continuous linear mapp... 详细信息

关键词： Dunkl Operators on Rd C∞-Functions on Rd Dunkl Intertwining Operator Mean-Periodic Functions Continuous Linear Mappings