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Riesz transforms for Dunkl transform [PDF]
Annales mathématiques Blaise Pascal, 2011 In this paper we obtain the $L^p$-boundedness of Riesz transforms for Dunkl transform for all ...
Amri, Béchir, Sifi, Mohamed
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Dunkl translations, Dunkl-type $BMO$ space and Riesz transforms for Dunkl transform on $L^\infty$
Functional Analysis and Its Applications, 2021 In this paper, we will give some results on the support of Dunkl translations on compactly supported functions. Then we will define Dunkl-type $BMO$ space and Riesz transforms for Dunkl transform on $L^\infty$, and prove the boundedness of Riesz ...
Teng, Wentao
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Paley-Wiener theorems for the Dunkl transform [PDF]
Transactions of the American Mathematical Society, 2005 We conjecture a geometrical form of the Paley-Wiener theorem for the Dunkl transform and prove three instances thereof, one of which involves a limit transition from Opdam's results for the graded Hecke algebra.
de Jeu, Marcel
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Inversion of the Dual Dunkl-Sonine Transform on R Using Dunkl Wavelets [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 We prove a Calder\'on reproducing formula for the Dunkl continuous wavelet transform on $\mathbb{R}$.
Mourou, Mohamed Ali
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Inversion Formulas for the Spherical Radon-Dunkl Transform [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 The spherical Radon-Dunkl transform $R_\kappa$, associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of $h$-harmonics.
Li, Zhongkai, Song, Futao
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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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Matrix Addition and the Dunkl Transform at High Temperature
Communications in Mathematical Physics, 2022 v2: added sections 1.4 and 4.1; fixed minor error in claim 9.1; added references. v3: 59 pages; added Sec. 3.4; added Conjecture 1.3 and Lemma 4.5; fixed a typo in last eqns.
Benaych-Georges, Florent +2 more
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Le Matematiche, 2013 In this paper, we introduce and study the q-Dunkl Sonine transform and we establish a Plancherel formula for its dual. Furthermore we give many inversion formulas.
Lassad Bennasr +2 more
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Riesz Potential and Maximal Function for Dunkl transform [PDF]
Potential Analysis, 2020 25 ...
D. V. Gorbachev +2 more
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Uncertainty principles for the Dunkl transform
Hiroshima Mathematical Journal, 2010 The uncertainty principle for the classical Fourier transform was proved by many mathematicians including Hardy and Beurling and its \(L^p\) version was proved by Cowling and Price. The above results for the Fourier transform were generalized to the Dunkl transform by Gallardo, Trimèche.
Hatem Mejjaoli
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