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
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. 3–14 (in Russian).
Differentiation operator, Stechkin's problem, Kolmogorov inequality.
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Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015), 20–29
Citation in format AMSBIB
\paper On the best approximation of the differentiation operator
\jour Ural Math. J.
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This publication is cited in the following articles:
V. V. Arestov, “Nailuchshee ravnomernoe priblizhenie operatora differentsirovaniya ogranichennymi v prostranstve $L_2$ operatorami”, Tr. IMM UrO RAN, 24, no. 4, 2018, 34–56
V. V. Arestov, “O sopryazhennosti prostranstva multiplikatorov”, Tr. IMM UrO RAN, 25, no. 4, 2019, 5–14
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