On trigonometric polynomials least deviating from zero

被引：3

作者：

Arestov, V. V. ^{[1
]}

Mendelev, A. S. ^{[2
]}

机构：

[1] Ural State Univ, Ekaterinburg 620083, Russia

[2] Russian Acad Sci, Inst Math & Mech, Ural Div, Ekaterinburg 620219, Russia

来源：

DOKLADY MATHEMATICS | 2009年 / 79卷 / 02期

关键词：

Real Line; Chebyshev Polynomial; DOKLADY Mathematic; Trigonometric Polynomial; Harmonic Measure;

D O I：

10.1134/S1064562409020343

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a solution of the problem about trigonometric polynomials with a given leading harmonic and least deviating from zero in measure; more precisely, with respect to the functional mu(f (n) ) = mes {t a [0, 2 pi]: |f (n) (t)| a parts per thousand yen 1}. We give a solution of a related problem about the minimal value over compact sets (from the real line) of a given measure of least uniform deviation from zero on a compact set for trigonometric polynomials with a fixed leading harmonic.

引用

页码：280 / 283

页数：4

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