RELATIVE WIDTH OF SMOOTH CLASSES OF MULTIVARIATE PERIODIC FUNCTIONS WITH RESTRICTIONS ON ITERATED LAPLACE DERIVATIVES IN THE L_2-METRIC

作     者：刘永平 杨连红 Liu Yongping School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China Yang Lianhong Department of Applied Mathematics, Communication University of China, Beijing 100024, China

作者机构：School of Mathematical Sciences Beijing Normal UniversityBeijing 100875China Department of Applied Mathematics Communication University of ChinaBeijing 100024China 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2006年第26卷第4期

页      面：720-728页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 

基　　金：Supported partly by National Natural Science Foundation of China (10471010) partly by the project "Representation Theory and Related Topics" of the "985 Program" of Beijing Normal University 

主　　题：Multivariate function classes width relative width 

摘      要：For two subsets W and V of a Banach space X, let Kn（W, V, X） denote the relative Kolmogorov n-width of W relative to V defined by Kn（W,V,X）：=inf sup inf/Ln f∈W g∈V∩Ln‖f-g‖x, where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2（△^τ） denote the class of 2π-periodic functions f with d-variables satisfying ∫[-π, π]^d｜△^τf（x）｜^2dx≤1, while △^τ is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2（△^τ） relative to W2（△^τ） in Lq（[-π, π]^d） （1≤ q ≤ ∞）, and obtain its weak asymptotic result.