Results 31 to 40 of about 2,908 (161)
Decomposition of Polyharmonic Functions with Respect to the Complex Dunkl Laplacian
Journal of Inequalities and Applications, 2010 Let Ω be a G-invariant convex domain in ℂN including 0, where G is a complex Coxeter group associated with reduced root system R⊂ℝN. We consider holomorphic functions f defined in Ω which are Dunkl polyharmonic, that
Guangbin Ren, Helmuth R. Malonek
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Capacity and the Corresponding Heat Semigroup Characterization from Dunkl-Bounded Variation
Fractal and Fractional, 2021 In this paper, we study some important basic properties of Dunkl-bounded variation functions. In particular, we derive a way of approximating Dunkl-bounded variation functions by smooth functions and establish a version of the Gauss–Green Theorem.
Xiangling Meng, Yu Liu, Xiangyun Xie
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The space of Dunkl monogenics associated with Z23
Nuclear Physics B, 2022 The universal Bannai–Ito algebra BI is a unital associative algebra over C generated by X,Y,Z and the relations assert that each of{X,Y}−Z,{Y,Z}−X,{Z,X}−Y commutes with X,Y,Z. Let n≥0 denote an integer.
Hau-Wen Huang
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On a vector-valued Hopf-Dunford-Schwartz lemma [PDF]
, 2011 In this paper, we state as a conjecture a vector-valued Hopf-Dunford-Schwartz lemma and give a partial answer to it. As an application of this powerful result, we prove some Fe fferman-Stein inequalities in the setting of Dunkl analysis where the ...
Charpentier, Stéphane, Deleaval, Luc
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On the Dunkl intertwining operator
Journal of Mathematical Analysis and Applications, 2017 Dunkl operators are differential-difference operators parametrized by a finite reflection group and a weight function. The commutative algebra generated by these operators generalizes the algebra of standard differential operators and intertwines with this latter by the so-called intertwining operator.
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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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Advances in Mathematical Physics, 2022 In this paper, we establish some new generalized results on the equivalence of K-functionals and modulus of continuity of functions defined on the Sobolev space Lα,β2ℝ, by using the harmonic analysis related to the Jacobi-Dunkl operator Δα,β, where α≥β ...
Ali El Mfadel +2 more
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Dunkl kernel associated with dihedral group
, 2015 In this paper, we pursue the investigations started in \cite{Mas-You} where the authors provide a construction of the Dunkl intertwining operator for a large subset of the set of regular multiplicity values. More precisely, we make concrete the action of
Deleaval, Luc +2 more
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Riesz transforms for Dunkl transform [PDF]
, 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 Operators: Theory and Applications [PDF]
, 2003 These lecture notes are intended as an introduction to the theory of rational Dunkl operators and the associated special functions, with an emphasis on positivity and asymptotics. We start with an outline of the general concepts: Dunkl operators, the intertwining operator, the Dunkl kernel and the Dunkl transform.
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