Comonotone approximation of periodic functions

被引：5

作者：

Dzyubenko, G. A. ^{[1
]}

Pleshakov, M. G. ^{[1
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Saratov, Russia

来源：

MATHEMATICAL NOTES | 2008年 / 83卷 / 1-2期

关键词：

2 pi-periodic function; comonotone approximation; trigonometric polynomial; Jackson kernel; Whitney's inequality;

D O I：

10.1134/S0001434608010203

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose that a continuous 2 pi-periodic function f on the real axis R changes its monotonicity at different ordered fixed points yi epsilon(-pi,pi), i = 1,..., 2s, s E epsilon N. In other words, there is a set Y := {yi}(i epsilon z) of points yi = y(i+2s) + 2 pi on R such that, on [y(i,)y(i-1)], f is nondecreasing if i is odd and nonincreasing if i is even. For each n >= N(Y), we construct a trigonometric polynomial P-eta of order <= n changing its monotonicity at the same points y(i) epsilon Y as f and such.

引用

页码：180 / 189

页数：10