Abstract:
We study the sharp inequality between the uniform norm and Lp(0,π/2)Lp(0,π/2)-norm of polynomials in the system C={cos(2k+1)x}∞k=0 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→∞ 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.
Bibliographic databases:
Document Type:
Article
Language: English
Citation:
Vitalii V. Arestov, Marina V. Deikalova, “On one inequality of different metrics for trigonometric polynomials”, Ural Math. J., 8:2 (2022), 27–45
\Bibitem{AreDei22}
\by Vitalii~V.~Arestov, Marina~V.~Deikalova
\paper On one inequality of different metrics for trigonometric polynomials
\jour Ural Math. J.
\yr 2022
\vol 8
\issue 2
\pages 27--45
\mathnet{http://mi.mathnet.ru/umj170}
\crossref{https://doi.org/10.15826/umj.2022.2.003}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4527689}
\elib{https://elibrary.ru/item.asp?id=50043140}
\edn{https://elibrary.ru/CUWFZK}
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https://www.mathnet.ru/eng/umj170
https://www.mathnet.ru/eng/umj/v8/i2/p27
This publication is cited in the following 2 articles:
V. V. Arestov, M. V. Deikalova, “A Generalized Translation Operator Generated by the Sinc Function on an Interval”, Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S32–S52
A. O. Leont'eva, “On Constants in the Bernstein–Szegő Inequality for the Weyl Derivative of Order Less Than Unity of Trigonometric Polynomials and Entire Functions of Exponential Type in the Uniform Norm”, Proc. Steklov Inst. Math. (Suppl.), 323, suppl. 1 (2023), S146–S154
Citation in format AMSBIB
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