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

This article is cited in 13 scientific papers (total in 13 papers)

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
Received: 02.06.1969

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
\by V.~N.~Gabushin
\paper Best approximations of functionals on certain sets
\jour Mat. Zametki
\yr 1970
\vol 8
\issue 5
\pages 551--562
\jour Math. Notes
\yr 1970
\vol 8
\issue 5
\pages 780--785

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    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  mathnet  crossref  mathscinet  zmath  isi
    2. V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    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  crossref  isi
    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  crossref  isi
    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  mathnet  crossref
    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  mathnet  crossref  mathscinet  isi  elib
    8. Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015), 20–29  mathnet  crossref  zmath
    9. R. R. Akopian, “Optimal Recovery of Analytic Functions from Boundary Conditions Specified with Error”, Math. Notes, 99:2 (2016), 177–182  mathnet  crossref  crossref  mathscinet  isi  elib
    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  mathnet  crossref  crossref  mathscinet  isi  elib
    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  crossref  isi
    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  mathnet  crossref  elib
    13. R. R. Akopyan, “An analogue of the two-constants theorem and optimal recovery of analytic functions”, Sb. Math., 210:10 (2019), 1348–1360  mathnet  crossref  crossref  adsnasa  isi  elib
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