Radouan Daher
YOU?
Author Swipe
View article: Heisenberg Type Inequality for the Continuous Laguerre Wavelet Transform
Heisenberg Type Inequality for the Continuous Laguerre Wavelet Transform Open
In this work, some uncertainty inequalities associated to the Laguerre wavelet transform are established. Namely, Donoho-Stark and Heisenberg-Weyl type uncertainty principles are proved.
View article: On the Jacobi-Dunkl coefficients of Lipschitz and Dini-Lipschitz functions on the circle
On the Jacobi-Dunkl coefficients of Lipschitz and Dini-Lipschitz functions on the circle Open
In this paper, we consider E the set of infinitely differentiable 2π -periodic functions on the circle T = R/2πZ .We use the distributions in E , as a tool to prove the continuity of the Jacobi-Dunkl operator.We obtain a generalization of …
View article: ON THE q-BESSEL TRANSFORM OF LIPSCHITZ AND DINI-LIPSCHITZ FUNCTIONS ON WEIGHTED SPACE Lp q,ν(R+ q)
ON THE q-BESSEL TRANSFORM OF LIPSCHITZ AND DINI-LIPSCHITZ FUNCTIONS ON WEIGHTED SPACE Lp q,ν(R+ q) Open
Titchmarsh proved some theorems (Theorems 84 and 85) on the classical Fourier transform of functions satisfying conditions related to the Cauchy-Lipschitz conditions in the one-dimensional case.In this paper, we obtain a generalization of …
View article: Laguerre-Bessel Transform and Generalized Lipschitz Classes
Laguerre-Bessel Transform and Generalized Lipschitz Classes Open
The aim of this paper is to give necessary and sufficient conditions in terms of the Fourier Laguerre-Bessel transform 𝒲 LB f of the function f to ensure that f belongs to the generalized Lipschitz classes H α k ( X ) and h k α ( X ), wher…
View article: An analog of Titchmarsh's theorem for the Laguerre–Bessel transform
An analog of Titchmarsh's theorem for the Laguerre–Bessel transform Open
Purpose Using a generalized translation operator, this study aims to obtain a generalization of Titchmarsh's theorem for the Laguerre–Bessel transform for functions satisfying the ψ-Laguerre–Bessel–Lipschitz condition in the space L 2 α ( …
View article: The Beurling theorem in space-time algebras
The Beurling theorem in space-time algebras Open
In this work, the space-time Fourier transform (SFT) introduced by E. Hitzer, satisfies some uncertainty principles of the algebra for space-time Cl (3,1) -valued signals over the space-time vector space R (3,1) . An analog of the Beurling…
View article: <i>K</i>-functional related to the Deformed Hankel Transform
<i>K</i>-functional related to the Deformed Hankel Transform Open
The main result of the paper is the proof of the equivalence theorem for a K -functional and a modulus of smoothness for the Deformed Hankel Transform. Before that, we introduce the K -functional associated to the Deformed Hankel Transform.
View article: A note of some approximation theorems of functions on the Laguerre hypergroup
A note of some approximation theorems of functions on the Laguerre hypergroup Open
This paper uses some basic notions and results on the Laguerre hypergroup K = [0, +?)xR to study some problems in the theory of approximation of functions in the space L2 ?(K). Analogues of the direct Jackson theorems of approximations for…
View article: Generalized Lipschitz and Besov spaces in terms of decay of Dunkl transforms in the space L2(Rd, wl(x)dx)
Generalized Lipschitz and Besov spaces in terms of decay of Dunkl transforms in the space L2(Rd, wl(x)dx) Open
For functions f ∈ L 2 (R d , wl (x)dx) with wl is a weight function invariant under the action of an associated Weyl group, we give necessary and sufficient conditions for f to belong to the generalized Lipschitz and Besov spaces in terms …
View article: Modulus of Smoothness and K-Functionals Constructed by Generalized Laguerre-Bessel Operator
Modulus of Smoothness and K-Functionals Constructed by Generalized Laguerre-Bessel Operator Open
In this paper, we prove the equivalence between a K-functional and a modulus of smoothness generated by Laguerre-Bessel operator on 𝕂 = [ 0 , + ∞ [ × [ 0 , + ∞ [ . \mathbb{K} = [0, + \infty [ \times [0, + \infty [.
View article: An analog of Hardy’s theorem for the second Hankel-Clifford transformation
An analog of Hardy’s theorem for the second Hankel-Clifford transformation Open
In this paper, we generalize theorem of Hardy for the second Hankel-Clifford transform .
View article: New estimates for the Fourier transform in the space L2(Rn)
New estimates for the Fourier transform in the space L2(Rn) Open
In this paper, we prove new estimates are presented for the integral \int_{|t|>N}|\widehat(f)(t)|^{2}dt, where \widehat(f) stands for the Fourier transform of f and N ≥ 1, in the space L2(Rn) characterized by the generalized modulus of con…
View article: On some theorems of the Jacobi-Lipschitz class for the Jacobi transform
On some theorems of the Jacobi-Lipschitz class for the Jacobi transform Open
Using a generalized Jacobi translation, we obtain a generalization of the theorem 84 of Titchmarsh for the Jacobi transform satisfying the Jacobi-Lipschitz and Dini Lipschitz conditions in the space Lp(R+; (t)dt), where 1 < p<= 2.
View article: On estimates for the Fourier-Bessel transform in the space Lp(R2+,x2α1+1y2α2+1dxdy)
On estimates for the Fourier-Bessel transform in the space Lp(R2+,x2α1+1y2α2+1dxdy) Open
In this paper, we prove two estimates useful in applications for the Fourier-Bessel transform in the space Lp(R2+,x2?1+1y2?2+1dxdy), (1 < p ? 2), as applied to some classes of functions characterized by a generalized modulus of continuity.
View article: Quantitative Uncertainty Principle for Sturm-Liouville Transform
Quantitative Uncertainty Principle for Sturm-Liouville Transform Open
In this paper we consider the Sturm-Liouville transform ℱ(f) on ℝ+. We analyze the concentration of this transform on sets of finite measure. In particular, Donoho-Stark and Benedicks-type uncertainty principles are given.
View article: Beurling’s Theorem for the Q-Fourier-Dunkl Transform
Beurling’s Theorem for the Q-Fourier-Dunkl Transform Open
The Q-Fourier-Dunkl transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. By using the heat kernel associated to the Q-Fourier-Dunkl operator, we establish an analogue of Beurling’s theorem for…
View article: Donoho-Stark Theorem For The Quadratic-Phase Fourier Integral Operators
Donoho-Stark Theorem For The Quadratic-Phase Fourier Integral Operators Open
In this paper, we obtain a generalization of the Donoho-Stark uncertainty principle associated with the Quadratic-Phase Fourier integral operators which is defined as a generalization of several integral transforms whose kernel has an expo…
View article: AN ANALOGUE OF COWLING-PRICE’S THEOREM FOR THE Q-FOURIER-DUNKL TRANSFORM
AN ANALOGUE OF COWLING-PRICE’S THEOREM FOR THE Q-FOURIER-DUNKL TRANSFORM Open
The Q-Fourier-Dunkl transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. By using theheat kernel associated to the Q-Fourier-Dunkl operator, we have established an analogue of Cowling-Price, …
View article: An extension of the Bessel–Wright transform in the class of Boehmians
An extension of the Bessel–Wright transform in the class of Boehmians Open
In this paper, we first construct a suitable Boehmian space on which the Bessel–Wright transform can be defined and some desired properties are obtained in the class of Boehmians. Some convergence results are also established.
View article: Некоторые оценки для обобщенного преобразования Фурье, ассоциированного с оператором Чередника - Опдама
Некоторые оценки для обобщенного преобразования Фурье, ассоциированного с оператором Чередника - Опдама Open
In the classical theory of approximation of functions on $\mathbb{R}^+$, the modulus of smoothness are basically built by means of the translation operators $f \to f(x+y)$. As the notion of translation operators was extended to various con…
View article: On estimates for the generalized Fourier-Bessel transform
On estimates for the generalized Fourier-Bessel transform Open
Two estimates useful in applications are proved for the generalized Fourier-Bessel transform in the space L2a,n as applied to some classes of functions characterized by a generalized modulus of continuity
View article: On Estimates for the Generalized Fourier-Dunkl Transform in the Space L2
On Estimates for the Generalized Fourier-Dunkl Transform in the Space L2 Open
Two useful estimates are proved for the generalized Fourier-Dunkltransform in the space L2 on certain classes of functions characterized by thegeneralized continuity modulus.
View article: Direct and inverse theorems of approximation theory
Direct and inverse theorems of approximation theory Open
In this paper, we prove analogues of direct and some inverse theorems, for the Dunkl harmonic analysis, using the function with bounded spectrum and generalized spherical mean operator.