This article is cited in 3 papers

On one inequality of different metrics for trigonometric polynomials

Vitalii V. Arestov^ab, Marina V. Deikalova<sup>ab

a</sup> Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
^b Ural Federal University

Abstract: We study the sharp inequality between the uniform norm and $L^p(0,\pi/2)$-norm of polynomials in the system $\mathscr{C}=\{\cos (2k+1)x\}_{k=0}^\infty$ of cosines with odd harmonics. We investigate the limit behavior of the best constant in this inequality with respect to the order $n$ of polynomials as $n\to\infty$ and provide a characterization of the extremal polynomial in the inequality for a fixed order of polynomials.

Keywords: trigonometric cosine polynomial in odd harmonics, Nikol'skii different metrics inequality.

Language: English

DOI: 10.15826/umj.2022.2.003

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