On the partial sums of a Fourier series

被引：7

作者：

Alzer, H. ^{[1
]}

Koumandos, S. ^{[1
]}

机构：

[1] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

来源：

CONSTRUCTIVE APPROXIMATION | 2008年 / 27卷 / 03期

关键词：

trigonometric polynomials; inequalities;

D O I：

10.1007/s00365-006-0665-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give sharp lower estimates for the partial sums of the Fourier series sin x + cos2x/2 + sin3x/ 3 + cos4x/4 + ... , with both an even and odd number of terms. Our results are obtained through a monotonicity property of their local minima. In particular, we prove that all partial sums are positive on (0, pi).

引用

页码：253 / 268

页数：16

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