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

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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. Arestov^ab

^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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Linking options:

https://www.mathnet.ru/eng/timm639

https://www.mathnet.ru/eng/timm/v16/i4/p38

This publication is cited in the following 11 articles:

A. O. Leont'eva, “Bernstein-Szegő inequality for the Riesz derivative of trigonometric polynomials in $L_p$ -spaces, $0\leqslant p\leqslant\infty$ , with classical value of the sharp constant”, Sb. Math., 214:3 (2023), 411–428
V. P. Zastavnyi, “Ob ekstremalnykh trigonometricheskikh polinomakh”, Tr. IMM UrO RAN, 29, no. 4, 2023, 70–91
A. O. Leonteva, “Neravenstvo Bernshteina - Sege dlya trigonometricheskikh polinomov v prostranstve $L_0$ s konstantoi bolshei, chem klassicheskaya”, Tr. IMM UrO RAN, 28, no. 4, 2022, 128–136
A. O. Serkov, “O neravenstve Segë — Taikova dlya sopryazhennykh trigonometricheskikh polinomov”, Tr. IMM UrO RAN, 21:4 (2015), 244–250
P. Yu. Glazyrina, “Szego-Taikov Inequality For Conjugate Polynomials”, Comput. Methods Funct. Theory, 15:4, SI (2015), 595–603
V. Arestov, M. Deikalova, “Nikol'skii Inequality Between the Uniform Norm and $L_q$ -Norm With Ultraspherical Weight of Algebraic Polynomials on An Interval”, Comput. Methods Funct. Theory, 15:4, SI (2015), 689–708
D. M. Kane, “Small Designs For Path-Connected Spaces and Path-Connected Homogeneous Spaces”, Trans. Am. Math. Soc., 367:9 (2015), 6387–6414
Ivan E. Simonov, Polina Yu. Glazyrina, “Sharp Markov–Nikol'skii inequality with respect to the uniform norm and the integral norm with Chebyshev weight”, Journal of Approximation Theory, 192 (2015), 69
E. D. Livshits, “A weak-type inequality for uniformly bounded trigonometric polynomials”, Proc. Steklov Inst. Math., 280 (2013), 208–219
V. V. Arestov, M. V. Deikalova, “Nikol'skii inequality for algebraic polynomials on a multidimensional Euclidean sphere”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 9–23
A. O. Leonteva, “Neravenstvo Bernshteina v $L_0$ dlya proizvodnoi nulevogo poryadka trigonometricheskikh polinomov”, Tr. IMM UrO RAN, 19, no. 2, 2013, 216–223

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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