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 Mat. Zametki, 1970, Volume 8, Issue 5, Pages 551–562 (Mi mz7003)

Best approximations of functionals on certain sets

V. N. Gabushin

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

Abstract: S. B. Stechkin's problem concerning the best approximation of an operator $U$ by bounded linear operators is investigated for the case in which $U$ is a functional. An upper bound is found for the discrepancy of the best approximation and properties of best approximating functionals are investigated. The results are used to study certain functionals related to the problem of finding the best approximation $E_N$ of the differentiation operator in $C(S)$, and the value of $E_N$ is calculated for all cases in which the exact value of the constant in the corresponding Kolmogorov inequality is known.

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English version:
Mathematical Notes, 1970, 8:5, 780–785

Bibliographic databases:

UDC: 517.5

Citation: V. N. Gabushin, “Best approximations of functionals on certain sets”, Mat. Zametki, 8:5 (1970), 551–562; Math. Notes, 8:5 (1970), 780–785

Citation in format AMSBIB
\Bibitem{Gab70} \by V.~N.~Gabushin \paper Best approximations of functionals on certain sets \jour Mat. Zametki \yr 1970 \vol 8 \issue 5 \pages 551--562 \mathnet{http://mi.mathnet.ru/mz7003} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=276665} \zmath{https://zbmath.org/?q=an:0243.41022} \transl \jour Math. Notes \yr 1970 \vol 8 \issue 5 \pages 780--785 \crossref{https://doi.org/10.1007/BF01146932} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. K. Yu. Osipenko, “Inequalities for derivatives of functions analytical in a strip”, Math. Notes, 56:4 (1994), 1069–1074
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. Babenko Yu. Skorokhodov D., “Stechkin's Problem for Differential Operators and Functionals of First and Second Orders”, J. Approx. Theory, 167 (2013), 173–200
5. Babenko V.F. Churilova M.S. Parfinovych N.V. Skorokhodov D.S., “Kolmogorov Type Inequalities For the Marchaud Fractional Derivatives on the Real Line and the Half-Line”, J. Inequal. Appl., 2014, 504
6. S. B. Vakarchuk, A. V. Shvachko, “Inequalities of Kolmogorov's type for derived functions in two variables and application to approximation by an “angle””, Russian Math. (Iz. VUZ), 59:11 (2015), 1–18
7. R. R. Akopian, “Optimal recovery of an analytic function in a doubly connected domain from its approximately given boundary values”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 13–18
8. Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015), 20–29
9. R. R. Akopian, “Optimal Recovery of Analytic Functions from Boundary Conditions Specified with Error”, Math. Notes, 99:2 (2016), 177–182
10. R. R. Akopyan, “Optimal recovery of a function analytic in a disk from approximately given values on a part of the boundary”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 25–37
11. Akopyan R.R., “Optimal Recovery of a Derivative of An Analytic Function From Values of the Function Given With An Error on a Part of the Boundary”, Anal. Math., 44:1 (2018), 3–19
12. V. V. Arestov, “Nailuchshee ravnomernoe priblizhenie operatora differentsirovaniya ogranichennymi v prostranstve $L_2$ operatorami”, Tr. IMM UrO RAN, 24, no. 4, 2018, 34–56
13. R. R. Akopyan, “An analogue of the two-constants theorem and optimal recovery of analytic functions”, Sb. Math., 210:10 (2019), 1348–1360
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