球型平移网络逼近周期函数  

Approxiamtion of Periodic Functions by Spherical Translation Networks

作　　者：盛宝怀[1] 

机构地区：[1]绍兴文理学院数学系,绍兴312000

出　　处：《数学学报（中文版）》2007年第1期55-62,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10471130);浙江省自然科学基金资助项目(Y604003)

摘　　要：研究了球型平移网络对周期函数的逼近问题．文章首先将基函数eimx分别表示成为两种球型平移网络．进一步,将有关多重Fourier级数的Bochner-Riesz平均表示成为球型平移网络的形式．在此基础上构造出了两类球型平移网络序列,并借助于有关Bochner-Riesz平均对Lp空间中函数的逼近结果给出了这两类球型平移网络序列在Lp空间中的逼近阶．In this paper, we investigate the approximation of periodic functions by translation networks formed by two kinds of spherical translations for a given periodic function. We first express the basis functions eimx as two kinds of spherical translation network sequences respectively. Secondly, the Bochner-Riesz means of multiple Fourier series are also expressed as spherical translation network sequences, with which two kinds of spherical translation network sequences are defined, and thirdly, the orders of approxiamtion in Lp spaces for these two kinds of spherical translation sequences are respectively given by making use of the approximation order of Bochner-Riesz means in Lp spaces.

关 键 词：周期函数 球平移网络 BOCHNER-RIESZ平均 

分 类 号：O174.41[理学—数学]