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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, Volume 28, Number 4, Pages 40–53
DOI: https://doi.org/10.21538/0134-4889-2022-28-4-40-53 (Mi timm1948) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On One Generalized Translation and the Corresponding Inequality of Different Metrics

V. V. Arestovab, M. V. Deikalovaba

a N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
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DOI: https://doi.org/10.21538/0134-4889-2022-28-4-40-53
Abstract: In this paper, we discuss the properties of the generalized translation operator generated by the system of functions $\left\{ \cos\left(\frac{(2k-1)\pi }{2}t\right)\right\}_{k=1}^\infty$ in the spaces $L^p(0,1)$, $p\ge 1$. The translation operator is applied to the study of the Nikol'skii inequality between the uniform norm and the $L^p$-norm of polynomials in this system.
Keywords: generalized translation operator, trigonometric polynomial, inequality of different metrics.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-874
This work was performed as a part of the research conducted in the Ural Mathematical Center and supported by the Ministry of Education and Science of the Russian Federation (agreement no. 075-02-2022-874).
Received: 05.06.2022
Revised: 05.07.2022
Accepted: 11.07.2022
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2022, Volume 319, Issue 1, Pages S30–S42
DOI: https://doi.org/10.1134/S0081543822060049
Bibliographic databases:
Document Type: Article
UDC: 517.518.86
MSC: 41A17
Language: Russian
Citation: V. V. Arestov, M. V. Deikalova, “On One Generalized Translation and the Corresponding Inequality of Different Metrics”, Trudy Inst. Mat. i Mekh. UrO RAN, 28, no. 4, 2022, 40–53; Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S30–S42
Citation in format AMSBIB
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\by V.~V.~Arestov, M.~V.~Deikalova
\paper On One Generalized Translation and the Corresponding Inequality of Different Metrics
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2022
\vol 28
\issue 4
\pages 40--53
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\crossref{https://doi.org/10.21538/0134-4889-2022-28-4-40-53}
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2022
\vol 319
\issue , suppl. 1
\pages S30--S42
\crossref{https://doi.org/10.1134/S0081543822060049}
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