This article is cited in 7 papers

On the best approximation of the differentiation operator

Vitalii V. Arestov<sup>ab

a</sup> 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. 3–14 (in Russian).

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

Language: English

DOI: 10.15826/umj.2015.1.002

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