ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATOR
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 (0 < k <n) are finite mea...
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| Format: | Article |
| Language: | English |
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Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
2015-11-01
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| Series: | Ural Mathematical Journal |
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| Online Access: | https://umjuran.ru/index.php/umj/article/view/34 |
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| author | Vitalii V. Arestov |
| author_facet | Vitalii V. Arestov |
| author_sort | Vitalii V. Arestov |
| collection | DOAJ |
| description | 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 (0 < k <n) are finite measures. We also determine the exact value of the best constant in the corresponding inequality for derivatives. |
| format | Article |
| id | doaj-art-1182411a8a09456e9a3069afbce99b5d |
| institution | DOAJ |
| issn | 2414-3952 |
| language | English |
| publishDate | 2015-11-01 |
| publisher | Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics |
| record_format | Article |
| series | Ural Mathematical Journal |
| spelling | doaj-art-1182411a8a09456e9a3069afbce99b5d2025-08-20T03:15:53ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522015-11-011110.15826/umj.2015.1.0022ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATORVitalii V. Arestov0Ural Federal University, Institute of Mathematics and Computer Science, Deparment of Mathematical Analysis and Function Theory, EkaterinburgIn 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 (0 < k <n) are finite measures. We also determine the exact value of the best constant in the corresponding inequality for derivatives.https://umjuran.ru/index.php/umj/article/view/34Differentiation operatorStechkin's problemKolmogorov inequality |
| spellingShingle | Vitalii V. Arestov ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATOR Ural Mathematical Journal Differentiation operator Stechkin's problem Kolmogorov inequality |
| title | ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATOR |
| title_full | ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATOR |
| title_fullStr | ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATOR |
| title_full_unstemmed | ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATOR |
| title_short | ON THE BEST APPROXIMATION OF THE DIFFERENTIATION OPERATOR |
| title_sort | on the best approximation of the differentiation operator |
| topic | Differentiation operator Stechkin's problem Kolmogorov inequality |
| url | https://umjuran.ru/index.php/umj/article/view/34 |
| work_keys_str_mv | AT vitaliivarestov onthebestapproximationofthedifferentiationoperator |