Results 21 to 30 of about 728,042 (147)

Uncertainty Principles for the Dunkl-Bessel type transform [PDF]

, 2022
The Dunkl-Bessel type transform satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Beurling’s theorem, Gelfand-Shilov theorem, Cowling-Price’s theorem and Morgan’s theorem are obtained for the Dunkl ...
Safouane, Najat, Radouan , Daher
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Semigroup and Riesz transform for the Dunkl–Schrödinger operators [PDF]

Semigroup Forum, 2020
Let $L_k=-Δ_k+V$ be the Dunk- Schrödinger operators, where $Δ_k=\sum_{j=1}^dT_j^2$ is the Dunkl Laplace operator associated to the dunkl operators $T_j$ on $\mathbb{R}^d$ and $V$ is a nonnegative potential function. In the first part of this paper we introduce the Riesz transform $R_j= T_j L_k^{-1/2}$ as an $L^2$- bounded operator and we prove that is ...
Amri, Béchir, Hammi, Amel
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Riesz transforms for the Dunkl harmonic oscillator [PDF]

Mathematische Zeitschrift, 2008
22 ...
Nowak, Adam, Stempak, Krzysztof
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Riesz transforms for Dunkl transform

Annales mathématiques Blaise Pascal, 2012
In this paper we obtain the L p -boundedness of Riesz transforms for the Dunkl transform for all 1
Amri, Bechir, Sifi, Mohamed
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Paley and Hardy's inequalities for the Fourier-Dunkl expansions [PDF]

Arab Journal of Mathematical Sciences
Purpose – Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based on a complete orthonormal system of Dunkl kernels generalizing the classical exponential system defining the classical Fourier series. Design/
Anis Elgarna
doaj   +1 more source

Analogues of Miyachi and Cowling-Price theorems for the generalized Dunkl transform [PDF]

, 2022
In this paper,we consider the generalized Dunkl transform which satisfies some uncertainty principles similar to the Euclidean Fourier transform. A generalization of Cowling-Price’s theorem, Miyachi’s theorem are obtained for the generalized Dunkl ...
Daher, Radouan, LOUALID, El Mehdi, Achak, Azzedine   +2 more
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Hörmander's multiplier theorem for the Dunkl transform [PDF]

Journal of Functional Analysis, 2019
For a normalized root system $R$ in $\mathbb R^N$ and a multiplicity function $k\geq 0$ let $\mathbf N=N+\sum_{α\in R} k(α)$. Denote by $dw(\mathbf x)=\prod_{α\in R}|\langle \mathbf x,α\rangle|^{k(α)}\, d\mathbf x $ the associated measure in $\mathbb R^N$. Let $\mathcal F$ stands for the Dunkl transform.
Dziubański, Jacek, Hejna, Agnieszka
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The multiplier of the interval [−1,1] for the Dunkl transform on the real line [PDF]

, 2007
We study the boundedness of the multiplier of the interval [−1,1] for the Dunkl transform of order α⩾−1/2 on weighted Lp spaces, with ...
Varona, Juan L., Betancor, Jorge J., Varona, J.L. [0000-0002-2023-9946], Ciaurri, Óscar, Ciaurri, O. [0000-0002-1695-3311], Betancor, J.J.   +5 more
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A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform [PDF]

, 2007
A Whittaker-Shannon-Kotel'nikov sampling theorem related to the Dunkl transform on the real line is proved. To this end we state, in terms of Bessel functions, an orthonormal system which is complete in L2((-1, 1), |x|2α+1 dx). This orthonormal system is
Varona, J.L. [0000-0002-2023-9946], Ciaurri, O. [0000-0002-1695-3311]   +1 more
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The dunkl transform

Inventiones mathematicae, 1993
In the late eighties, Dunkel found a remarkable set of commuting operators that can be associated with a finite real reflection group. The operators contain complex parameters; if these parameters are all zero, Dunkl's operators reduce to the ordinary directional derivatives.
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