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 Mat. Zametki, 1968, Volume 3, Issue 2, Pages 157–164 (Mi mz6662)

Best approximation of a differentiation operator in $L_2$-space

Yu. N. Subbotin, L. V. Taikov

V. A. Steklov Institute of Mathematics, Sverdlovsk Branch of the Academy of Sciences of USSR

Abstract: This paper contains the magnitude of the best approximation in the $L_2$-sense of a $k$-th order differentiation operator of a bounded linear operator $A(f)$ which acts on the class of functions which are differentiable $n$ times.

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English version:
Mathematical Notes, 1968, 3:2, 106–109

Bibliographic databases:

UDC: 517.5

Citation: Yu. N. Subbotin, L. V. Taikov, “Best approximation of a differentiation operator in $L_2$-space”, Mat. Zametki, 3:2 (1968), 157–164; Math. Notes, 3:2 (1968), 106–109

Citation in format AMSBIB
\Bibitem{SubTai68} \by Yu.~N.~Subbotin, L.~V.~Taikov \paper Best approximation of a~differentiation operator in $L_2$-space \jour Mat. Zametki \yr 1968 \vol 3 \issue 2 \pages 157--164 \mathnet{http://mi.mathnet.ru/mz6662} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=228892} \zmath{https://zbmath.org/?q=an:0172.40004} \transl \jour Math. Notes \yr 1968 \vol 3 \issue 2 \pages 106--109 \crossref{https://doi.org/10.1007/BF01094328} 

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This publication is cited in the following articles:
1. B. E. Klots, “Best linear and nonlinear approximations for smooth functions”, Funct. Anal. Appl., 12:1 (1978), 12–19
2. V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126
3. V. V. Arestov, “The best approximation to a class of functions of several variables by another class and related extremum problems”, Math. Notes, 64:3 (1998), 279–294
4. A. A. Koshelev, “The best approximation of Laplace operator by linear bounded operators in the space $L_p$”, Russian Math. (Iz. VUZ), 55:6 (2011), 53–63
5. “Yurii Nikolaevich Subbotin. (K semidesyatipyatiletiyu so dnya rozhdeniya)”, Tr. IMM UrO RAN, 17, no. 3, 2011, 8–13
6. V. V. Arestov, M. A. Filatova, “On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 24–40
7. V. V. Arestov, M. A. Filatova, “Approximation of differentiation operator in the space $L_2$ on semiaxis”, Russian Math. (Iz. VUZ), 57:5 (2013), 1–8
8. Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015), 20–29
9. Babenko V. Babenko Yu. Kriachko N., “Inequalities of Hardy–Littlewood–Polya type for functions of operators and their applications”, J. Math. Anal. Appl., 444:1 (2016), 512–526
10. V. V. Arestov, “Nailuchshee ravnomernoe priblizhenie operatora differentsirovaniya ogranichennymi v prostranstve $L_2$ operatorami”, Tr. IMM UrO RAN, 24, no. 4, 2018, 34–56
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