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

作     者：Yong Ping LIU Chun Yuan SONG 

作者机构：School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2014年第30卷第10期

页      面：1748-1762页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by National Natural Science Foundation of China(Grant No.11071019) the research Fund for the Doctoral Program of Higher Education and Beijing Natural Science Foundation(Grant No.1102011) 

主　　题：Reflection group Dunkl transform Bessel function Jackson inequality continuous modulus 

摘      要：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.