文献类型：期刊文献

中文题名：球型平移网络逼近周期函数

英文题名：Approxiamtion of Periodic Functions by Spherical Translation Networks

作者：盛宝怀[1]

机构：[1]绍兴文理学院数学系

年份：2007

卷号：50

期号：1

起止页码：55

中文期刊名：数学学报：中文版

收录：CSTPCD、、北大核心2004、Scopus、CSCD2011_2012、北大核心、CSCD

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)

语种：中文

中文关键词：周期函数;球平移网络;Bochner-Riesz平均

外文关键词：periodic function; spherical translation networks; Bochner-Riesz means

中文摘要：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．

外文摘要：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.