Fethi Soltani

Inversion formulas in the Dunkl-type heat conduction on

We study the generalized Gaussian convolution associated with the Dunkl operators. Next we shall give practical real inversion formulas of Dunkl-type heat conduction on .

Practical inversion formulas in a quantum mechanical system

This article deals with the operator The operator P appears in quantum mechanics on the 1-sphere S 1 based on Dirac formalism. On the basis of an integral transform W constructed by S. Watanabe and using the theory of reproducing kernels, we shall give approximate practical real inversion formulas in a quantum mechanical system.This article deals with the operator The operator P appears in quantum mechanics on the 1-sphere S 1 based on Dirac formalism. On the basis of an integral transform W constructed by S. Watanabe and using the theory of reproducing kernels, we shall give approximate practical real inversion formulas in a quantum mechanical system.

Analytical and numerical applications for the Fourier multiplier operators on ℝn × (0, ∞)

We study the Fourier multiplier operators , where and ; and we establish for them some versions of uncertainty principles. Moreover, we give an application of the general theory of reproducing kernels to the Tikhonov regularization for . Meanwhile, we give the approximate formulas for on a Hilbert space . Further, we shall establish error estimates for our approximation formulas. Finally, by using computers, we shall illustrate numerical experiments approximation formulas in .

Operators and Tikhonov regularization on the Fock space

In this work, we study the boundedness of some operators on the Fock space F and give an application of the theory of reproducing kernels to the Tikhonov regularization, which gives the approximate solutions for bounded linear operator equations on the Fock space F.

Inversion formulas for the Dunkl-type Segal–Bargmann transform

We give the inverse of the Dunkl-type Segal–Bargmann transform as a limit of certain integral operators. An application to Tikhonov regularization on the Dunkl-type Fock spaces is given using the theory of reproducing kernel Hilbert spaces.

Dunkl multiplier operators and applications

We study some class of Dunkl multiplier operators; and we establish for them some versions of uncertainty principles. For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev–Dunkl spaces.

L P LOCAL UNCERTAINTY INEQUALITY FOR THE STURM-LIOUVILLE TRANSFORM

Department of Mathematics, Faculty of Science,Jazan University,P.O.Box 114, Jazan, Kingdom of Saudi Arabia.fethisoltani10@yahoo.comABSTRACTIn this paper, we give analogues of local uncertainty inequality for the Sturm-Liouvilletransform on [0,∞[. A generalization of Donoho-Stark’s uncertainty principle is ob-tained for this transform.RESUMENEn este art´iculo entregamos resultados an´alogos de una desigualdad de incertidumbrelocal de la transformada Sturm-Liouville en [0,∞[. Una generalizaci´on del principio deincertidumbre de Donoho-Stark se obtiene de esta transformaci´on.Keywords and Phrases: Sturm-Liouville transform; local uncertainty principle; Donoho-Stark’suncertainty principle.2010 AMS Mathematics Subject Classification: 42B10; 44A20; 46G12.

Reproducing inversion formulas for the Dunkl-Wigner transforms

fethisoltani10@yahoo.comABSTRACTWe define and study the Fourier-Wignertransformassociated with the Dunkl operators,and we prove for this transform a reproducing inversion formulas and a Plancherelformula. Next, we introduce and study the extremal functions associated to the Dunkl-Wigner transform.RESUMENDefinimos y estudiamos la transformada de Fourier-Wigner asociada a los operadoresde Dunkl, y probamos una formula de inversion y una formula de Plancherel para estatransformada. Luego introducimos y estudiamos las funciones extramales asociadas ala transformada de Dunkl-Wigner.Keywords and Phrases: Dunkl transform; Dunkl-Wigner transform; inversion formulas; ex-tremal functions.2010 AMS Mathematics Subject Classification: 42B10; 44A20; 46F12.

Pitt's inequalities for the Dunkl transform on ℝd

We show Stein–Weiss inequality and Hardy–Littlewood–Sobolev inequality in the Dunkl setting; and we deduce some versions of Pitts inequality for the Dunkl transform on ℝd.

Fock-type spaces associated to higher-order Bessel operator

ABSTRACT In this paper we study the Fock-type space of analytic functions on the plane, invariant with respect to rotations of the plane by , with weight generated in a special way from the solutions of the higher-order Bessel equation. We give an explicit construction of the Bergman kernel for this space; and we prove that the operator of multiplication by is adjoint in this space to the higher-order Bessel operator. These instruments are used to investigate, in this new setting, some standard properties of operators in this space, including the basic properties of Toeplitz and Hankel operators, the uncertainty property and extremal functions for some operators.