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Ural Math. J., 2015, Volume 1, Issue 1, Pages 20–29 (Mi umj2)  

This article is cited in 2 scientific papers (total in 2 papers)

On the best approximation of the differentiation operator

Vitalii V. Arestovab

a Institute of Mathematics and Computer Science, Ural Federal University, Yekaterinburg, Russia
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia

Abstract: In this paper we give a solution of the problem of the best approximation in the uniform norm of the differentiation operator of order k by bounded linear operators in the class of functions with the property that the Fourier transforms of their derivatives of order $n$ $(t<k<n)$ are finite measures. We also determine the exact value of the best constant in the corresponding inequality for derivatives.
The paper was originally published in a hard accessible collection of articles Approximation of Functions by Polynomials and Splines (UNTs AN SSSR, Sverdlovsk, 1985), p. 314 (in Russian).

Keywords: Differentiation operator, Stechkin's problem, Kolmogorov inequality.

DOI: https://doi.org/10.15826/umj.2015.1.002

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Full text: http://umjuran.ru/.../34
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Citation: Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015), 20–29

Citation in format AMSBIB
\Bibitem{Are15}
\by Vitalii~V.~Arestov
\paper On the best approximation of the differentiation operator
\jour Ural Math. J.
\yr 2015
\vol 1
\issue 1
\pages 20--29
\mathnet{http://mi.mathnet.ru/umj2}
\crossref{https://doi.org/10.15826/umj.2015.1.002}
\zmath{https://zbmath.org/?q=an:1396.41018}
\elib{https://elibrary.ru/item.asp?id=25613592}


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

    This publication is cited in the following articles:
    1. V. V. Arestov, “Nailuchshee ravnomernoe priblizhenie operatora differentsirovaniya ogranichennymi v prostranstve $L_2$ operatorami”, Tr. IMM UrO RAN, 24, no. 4, 2018, 34–56  mathnet  crossref  elib
    2. V. V. Arestov, “O sopryazhennosti prostranstva multiplikatorov”, Tr. IMM UrO RAN, 25, no. 4, 2019, 5–14  mathnet  crossref  elib
  • Ural Mathematical Journal
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