Sharp Inequalities for Trigonometric Polynomials With Respect to Integral Functionals

被引：0

作者：

Arestov, V. V. ^{[1
,2
]}

机构：

[1] Russian Acad Sci, Inst Math & Mech, Ural Branch, Phys Mat Sci, Moscow, Russia

[2] Russian Acad Sci, Inst Math & Mech, Ural Branch, Moscow, Russia

来源：

TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN | 2010年 / 16卷 / 04期

关键词：

sharp inequalities for trigonometric polynomials; integral functional; trigonometric polynomials that deviate the least from zero;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The problem on sharp inequalities for linear operators on the set of trigonometric polynomials with respect to integral functionals integral(2 pi)(0)phi(vertical bar f(x)vertical bar)dx is discussed. A solution of the problem on trigonometric polynomials with given leading harmonic that deviate the least from zero with respect to such functionals over the set of all functions phi determined, nonnegative, and nondecreasing on the semi-axis [0, +infinity) is given.

引用

页码：38 / 53

页数：16

共 50 条

[1] Sharp Inequalities for Trigonometric Polynomials with Respect to Integral Functionals
Arestov, V. V.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2011, 273 : S21 - S36
[2] Sharp inequalities for trigonometric polynomials with respect to integral functionals
V. V. Arestov
Proceedings of the Steklov Institute of Mathematics, 2011, 273 : 21 - 36
[3] Sharp integral inequalities for fractional derivatives of trigonometric polynomials
Arestov, Vitalii V.
Glazyrina, Polina Yu.
JOURNAL OF APPROXIMATION THEORY, 2012, 164 (11) : 1501 - 1512
[4] Integral inequalities for algebraic and trigonometric polynomials
V. V. Arestov
P. Yu. Glazyrina
Doklady Mathematics, 2012, 85 : 104 - 108
[5] Integral inequalities for algebraic and trigonometric polynomials
Arestov, V. V.
Glazyrina, P. Yu.
DOKLADY MATHEMATICS, 2012, 85 (01) : 104 - 108
[6] Inequalities for trigonometric polynomials in spaces with integral metric
Pichugov, S. A.
UKRAINIAN MATHEMATICAL JOURNAL, 2012, 63 (12) : 1883 - 1899
[7] Inequalities for trigonometric polynomials and some integral means
Knoop, HB
Zhou, XL
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 255 (01) : 147 - 162
[8] Inequalities for trigonometric polynomials in spaces with integral metric
S. A. Pichugov
Ukrainian Mathematical Journal, 2012, 63 : 1883 - 1899
[9] ON INTEGRAL-INEQUALITIES FOR TRIGONOMETRIC POLYNOMIALS AND THEIR DERIVATIVES
ARESTOV, VV
MATHEMATICS OF THE USSR-IZVESTIYA, 1981, 45 (01): : 1 - 17
[10] Asymptotically sharp Markov-type inequalities for trigonometric and algebraic polynomials
Kalmykov, S. I.
MATHEMATICAL NOTES, 2015, 98 (1-2) : 331 - 335

← 1 2 3 4 5 →