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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2010, Volume 16, Number 4, Pages 38–53 (Mi timm639)  
This article is cited in 11 scientific papers (total in 11 papers)

Sharp inequalities for trigonometric polynomials with respect to integral functionals

V. V. Arestovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural State University
Full-text PDF (227 kB) Citations (11)
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Abstract: The problem on sharp inequalities for linear operators on the set of trigonometric polynomials with respect to integral functionals $\int_0^{2\pi}\varphi(|f(x)|)\,dx$ 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 $\varphi$ determined, nonnegative, and nondecreasing on the semi-axis $[0,+\infty)$ is given.
Keywords: sharp inequalities for trigonometric polynomials, integral functional, trigonometric polynomials that deviate the least from zero.
Received: 10.08.2010
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, Volume 273, Issue 1, Pages S21–S36
DOI: https://doi.org/10.1134/S0081543811050038
Bibliographic databases:
Document Type: Article
UDC: 517.518.86
Language: Russian
Citation: V. V. Arestov, “Sharp inequalities for trigonometric polynomials with respect to integral functionals”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 38–53; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S21–S36
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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