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. 3–14 (in Russian).
\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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This publication is cited in the following 7 articles:
Vitalii V. Arestov, “Approximation of differentiation operators by bounded linear operators in lebesgue spaces on the axis and related problems in the spaces of (p,q)-multipliers and their predual spaces”, Ural Math. J., 9:2 (2023), 4–27
V. V. Arestov, “Predual Spaces for the Space of (p, q)-Multipliers and Their Application in Stechkin's Problem on Approximation of Differentiation Operators”, Anal Math, 49:1 (2023), 43
K. Yu. Osipenko, “Optimal recovery in weighted spaces with homogeneous weights”, Sb. Math., 213:3 (2022), 385–411
V. V. Arestov, R. R. Akopyan, “Zadacha Stechkina o nailuchshem priblizhenii neogranichennogo operatora ogranichennymi i rodstvennye ei zadachi”, Tr. IMM UrO RAN, 26, no. 4, 2020, 7–31
V. Arestov, “Uniform Approximation of Differentiation Operators by Bounded Linear Operators in the Space Lr”, Anal Math, 46:3 (2020), 425
V. V. Arestov, “O sopryazhennosti prostranstva multiplikatorov”, Tr. IMM UrO RAN, 25, no. 4, 2019, 5–14
V. V. Arestov, “Best Uniform Approximation of the Differentiation Operator by Operators Bounded in the Space L2”, Proc. Steklov Inst. Math. (Suppl.), 308, suppl. 1 (2020), S9–S30
Citation in format AMSBIB
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