On approximation by rational functions with prescribed numerator degree in LP spaces

被引：5

作者：

Yu, D. S. ^{[1
]}

Zhou, S. P. ^{[1
]}

机构：

[1] Zhejiang Sci Tech Univ, Inst Math, Xiasha Econ Dev Area, Hangzhou 310018, Zhejiang, Peoples R China

来源：

ACTA MATHEMATICA HUNGARICA | 2006年 / 111卷 / 03期

基金：

中国国家自然科学基金;

关键词：

rational function; prescribed numerator degree; L-P space; approximation rate;

D O I：

10.1007/s10474-006-0051-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that, if f (x) is an element of L-[-1,1](p), < p < infinity, changes sign exactly l times, then there exists a real rational function r(x) is an element of R-n(l) such that parallel to f-r parallel to(p) <= C-p,C-delta(l + 1)(2) omega(f, (n-1))(p), which generalizes a result of Leviatan and Lubinsky in [2]. A weaker similar result in L-[-1,1](1) is also established.

引用

页码：221 / 236

页数：16

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