Limit theory of restricted range approximations of complex-valued continuous functions  

作　　者：Xian-fa LUO~1 Chong LI~(2+) ~1 School of Mathematics and Computer Science,Jishou University,Jishou 416000,China ~2 Department of Mathematics,Zhejiang University,Hangzhou 310027,China 

出　　处：《Science China Mathematics》2007年第10期1427-1440,共14页中国科学：数学（英文版）

基　　金：This work was partially supported by the National Natural Science Foundation of China(Grant No.10671175);the Program for New Century Excellent Talents in University and the Scientific Research Fund of Hunan Provincial Education Department(Grant No.06C651)

摘　　要：This paper is concerned with the problem of the best restricted range approximations of complex-valued continuous functions. Several properties for the approximating set PΩ such that the classical characterization results and/or the uniqueness results of the best approximations hold are introduced. Under the very mild conditions, we prove that these properties are equivalent that P is a Haar subspce.This paper is concerned with the problem of the best restricted range approximations of complex-valued continuous functions.Several properties for the approximating set P_Ωsuch that the classical characterization results and/or the uniqueness results of the best approximations hold are introduced.Under the very mild conditions,we prove that these properties are equivalent that P is a Haar subspce.

关 键 词：RESTRICTED RANGE approximation  HAAR subspace  characterization  UNIQUENESS 

分 类 号：O174[理学—数学]