STRONG UNIQUENESS OF GENERALIZED P0LYNOMIAL OF BEST APPROXIMATION HAVING BOUNDED COEFFICIENTS  

作　　者：XU SHUSHENG 许树声(Jiangnan University)

机构地区：[1]Jiangnan University

出　　处：《Acta Mathematicae Applicatae Sinica》1991年第1期17-33,共17页应用数学学报(英文版)

摘　　要：Let the set of generalized polynomials haviug bounded coefficients be K={p=■a_(j)g_(j):α_(j)■[α_(j),β_(j)],j=1,2,…,n}where g_1,g_2,…,g_n are linearly independent continuous functions defined on the interval[a,b],α_(j)β_(j),are extended real numbers satisfyingα_(j)<+∞,β_(j)>?andα_(j)≤β_(j).Assume that f is a continuousfunction defined on a compact set X[a,b].In the paper,we first give the sufficient conditions forthe polynomial of best uniform approxmation to f from K being unique and strongly unique.Furthermore,we give two forms of necessary and sufficient conditions for the best approximationto be strongly unique.

分 类 号：O1[理学—数学]