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On Some Theorems of the Dunkl—Lipschitz Class for the Dunkl Transform

Lobachevskii Journal of Mathematics, 2019
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Mohamed El Hamma, Radouan Daher
exaly   +5 more sources

Solution of Integral Equations by Dunkl and Distributional Dunkl Transform

Journal of the Indian Mathematical Society, 2018
The paper investigates the Dunkl transform and distributional Dunkl transform and the basic properties as convolution. The integral equations such as Volterra integral equation of first and second kind and Abel integral equation are solved by using dunkl transform.
Deshna Loonker
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Weyl Transforms Associated with Dunkl Wavelet Transform

Complex Analysis and Operator Theory, 2023
In this paper, the authors define Weyl transforms using the admissible wavelet associated with the Dunkl transform, and provide several inequalities using the Dunkl wavelet transform. They mainly prove that the Weyl transform \(W_\rho\) is bounded and compact for \(p \in [1, 2]\), and unbounded for \(p > 2\).
Akhilesh Prasad
exaly   +2 more sources

Uncertainty Principles for the Continuous Dunkl Gabor Transform and the Dunkl Continuous Wavelet Transform

Mediterranean Journal of Mathematics, 2008
In this paper we consider the Dunkl operators Tj, j = 1, . . . , d, on \(\mathbb {R}^d\) and the harmonic analysis associated with these operators. We define a continuous Dunkl Gabor transform, involving the Dunkl translation operator, by proceeding as mentioned in [20] by C.Wojciech and G. Gigante.
Hatem Mejjaoli
exaly   +2 more sources

Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators

Integral Transforms and Special Functions, 2002
We use the Dunkl intertwining operator V_k and its dual ^tV_k to prove a Paley-Wiener theorem for the Dunkl transform, for functions and distributions, and geometric forms of this theorem. These operators permit also to define and study Dunkl translation operators and Dunkl convolution product.
exaly   +2 more sources

Wavelet transform associated with Dunkl transform

Integral Transforms and Special Functions
Akhilesh Prasad, Randhir Kumar Verma
exaly   +2 more sources

A transference theorem for the Dunkl transform and its applications [PDF]

Journal of Functional Analysis, 2010
For a family of weight functions invariant under a finite reflection group, we show how weighted Lp multiplier theorems for Dunkl transform on the Euclidean space Rd can be transferred from the corresponding results for h-harmonic expansions on the unit ...
Heping Wang, Feng Dai
exaly   +2 more sources

The Dunkl-Hausdorff operators and the Dunkl continuous wavelets transform

Journal of Pseudo-Differential Operators and Applications, 2020
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Radouan Daher, Faouaz Saadi
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Nondeformed Generalized Dunkl Transform on the Line

Mathematical Notes, 2023
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Boundedness of Dunkl–Riesz transforms on Dunkl–Besov spaces

Illinois Journal of Mathematics
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Lee, Ming-Yi, Lin, Chin-Cheng, Ooi, Keng Hao   +2 more
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