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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
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
Аннотация:
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).
Ключевые слова:
Differentiation operator, Stechkin's problem, Kolmogorov inequality.
Образец цитирования:
Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015), 20–29
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/umj2 https://www.mathnet.ru/rus/umj/v1/i1/p20
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Страница аннотации: | 260 | PDF полного текста: | 89 | Список литературы: | 42 |
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