赋范线性空间的限制逼近及其应用  

RESTRICTED APPROXIMATIONS IN NORMED LINEAR SPACES AND THEIR APPLICATIONS

作　　者：李冲 

机构地区：[1]杭州商学院

出　　处：《应用数学学报》1990年第3期296-303,共8页Acta Mathematicae Applicatae Sinica

摘　　要：这里A是某个紧Hausdorff空间,l,u∈C（A）.G是由{h1,…,hn}张成的n维子空间,且满足下述条件: i)hi是定义在T∪A上的函数,且在T上,hi∈Lpw（T,μ）,在A上连续（i=1,2,…,n）。 ii){hi}in=1在T和A上分别是线性无关的.This paper discusses the problem of best approximations by elements with linear restrictionin normed linear spaces. The existence theorem, characterization theorems and uniqueness theo-rems are stated. Furthermore, as applications, the characterization of best L_p approximations byfunctions with restricted ranges, and the uniqueness of best L approximations by polynomialshaving bounded coefficients or restricted ranges of their derivatives are obtained.

关 键 词：赋范线性空间 限制逼近 极小问题 

分 类 号：O174.41[理学—数学]