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MULTIPLIER OPERATORS AND EXTREMAL FUNCTIONS RELATED TO THE DUAL dunkl-SONINE OPERATOR

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Acta Mathematica Scientia 2013年第2期33卷 430-442页

作者： Fethi SOLTANI Higher College of Technology and Informatics Street of the Employers 45Charguia 2 - 2035 TunisTunisia

We study the dual dunkl-Sonine operator tSk,e on Rd and give expression of tSk,t, using dunkl multiplier operators on Rd, Next, we study the extremal functions fλ, λ〉 0 related to the dunkl multiplier operators, and more precisely show that {fλ}λ〉0 converges uniformly to tSk,e（f） as λ→0 Certain examples based on dunkl-heat and Dunkt-Poisson kernels are provided to illustrate the results.

关键词： dunkl transform dual dunkl-Sonine operator multiplier operators extremalfunction

dunkl's Theory and Best Approximation by Entire Functions of Exponential Type in L_2-metric with Power Weight

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Acta Mathematica Sinica,English Series 2014年第10期30卷 1748-1762页

作者： Yong Ping LIU Chun Yuan SONG School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education

In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L2,k（Rd） by a subspace Ek2（σ）（SEk2（σ））, which is a subspace of entire functions of exponential type （spherical exponential type） at most σ. Here L2,k（Rd） denotes the space of all d-variate functions f endowed with the L2-norm with the weight vk（x）=Пζ∈R＋}（ζ,x）}2k（ζ）,which is defined by a positive subsystem R＋ of a finite root system R Rd and a function k（ζ）：R→R＋ invariant under the reflection group G（R） generated by R. In the case G（R） = Z2d, we get some exact results. Moreover, the deviation of best approximation by the subspace Ek2（σ）（SE2（σ）） of some class of the smooth functions in the space L2,k（Rd） is obtained.

关键词： Reflection group dunkl transform Bessel function Jackson inequality continuous modulus

DUALITY OF GENERALIZED dunkl-LIPSCHITZ SPACES

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Acta Mathematica Scientia 2017年第6期37卷 1567-1593页

作者： Samir KALLEL Department of Mathematics Higher Institute of Computer Sciences and Mathematics of MonastirMonastir University5000 MonastirTunisia

Abstract The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces ∧κα,p,q（R）, α ∈R and 1≤〈 p, q ≤∞, in the context of dunkl harmonic analysis.

关键词： dunkl operator duality Herz spaces heat transform dunkl transform gen-eralized dunkl-Lipschitz spaces

BoundaryValues of Generalized Harmonic Functions Associated with the Rank-One dunkl Operator

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Analysis in Theory and Applications 2020年第3期36卷 326-347页

作者： Jiaxi Jiu Zhongkai Li Department of Mathematics Shanghai Normal UniversityShanghai 200234China

We consider the local boundary values of generalized harmonic functions associated with the rank-one dunkl operator D in the upper half-plane R2+=R×(0,∞),where(Df)(x)=f′0(x)+(λ/x)[f(x)-f(-x)]for givenλ≥0.A C2 function u in R2+is said to beλ-harmonic if(D2x+■2y)u=*** aλ-harmonic function u in R2+and for a subset E of■R2+=R symmetric about y-axis,we prove that the following three assertions are equivalent:(i)u has a finite non-tangential limit at(x,0)for a.e.x∈E;(ii)u is non-tangentially bounded for a.e.x∈E;(iii)(Su)(x)dunkl operator D.

关键词： dunkl operator dunkl transform harmonic function non-tangential limit area integral.