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

This article is cited in 9 scientific papers (total in 10 papers)

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.

Full text: PDF file (356 kB)

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

Bibliographic databases:

UDC: 517.5
Received: 16.10.1967

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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    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. B. E. Klots, “Best linear and nonlinear approximations for smooth functions”, Funct. Anal. Appl., 12:1 (1978), 12–19  mathnet  crossref  mathscinet  zmath
    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. 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  mathnet  crossref  mathscinet  elib
    5. “Yurii Nikolaevich Subbotin. (K semidesyatipyatiletiyu so dnya rozhdeniya)”, Tr. IMM UrO RAN, 17, no. 3, 2011, 8–13  mathnet
    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  mathnet  crossref  isi  elib
    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  mathnet
    8. Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015), 20–29  mathnet  crossref  zmath
    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  crossref  mathscinet  zmath  isi  elib  scopus
    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  mathnet  crossref  elib
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