V. N. Gabushin, “The best approximation of the differentiation operator in the metric of $L_p$”, Mat. Zametki, 12:5 (1972), 531–538; Math. Notes, 12:5 (1972), 756

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Matematicheskie Zametki, 1972, Volume 12, Issue 5, Pages 531–538 (Mi mzm9913)

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

The best approximation of the differentiation operator in the metric of

$L_p$

V. N. Gabushin

Institute of Mathematics and Mechanics, Academy of Sciences of the USSR

Full-text PDF (850 kB) Citations (9)

Abstract: For Stechkin's problem of the best approximation for the differentiation operator

$E_n=\inf_{\substack{L_q\\ ||V||_{L_p}\leqslant n}}\sup_{||f^{(l)}||_{L_r(S)}\leqslant 1}||f^{(k)}-Vf||_{L_q(S)}$
we indicate the necessary and sufficient conditions that

$E_n$ be finite. We study some properties of continuous linear operators

$V$ from

$L_p$ into

$L_q$ .

Received: 20.09.1971

English version:
Mathematical Notes, 1972, Volume 12, Issue 5, Pages 756–760
DOI: https://doi.org/10.1007/BF01099059

Bibliographic databases:

Document Type: Article

UDC: 517.4

Language: Russian

Citation: V. N. Gabushin, “The best approximation of the differentiation operator in the metric of

$L_p$ ”, Mat. Zametki, 12:5 (1972), 531–538; Math. Notes, 12:5 (1972), 756–760

Citation in format AMSBIB

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\by V.~N.~Gabushin

\paper The best approximation of the differentiation operator in the metric of~$L_p$

\jour Mat. Zametki

\yr 1972

\vol 12

\issue 5

\pages 531--538

\mathnet{http://mi.mathnet.ru/mzm9913}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=324277}

\zmath{https://zbmath.org/?q=an:0262.41018}

\transl

\jour Math. Notes

\yr 1972

\vol 12

\issue 5

\pages 756--760

\crossref{https://doi.org/10.1007/BF01099059}

Linking options:

https://www.mathnet.ru/eng/mzm9913

https://www.mathnet.ru/eng/mzm/v12/i5/p531

This publication is cited in the following 9 articles:

Vitalii V. Arestov, “Approximation of differentiation operators by bounded linear operators in lebesgue spaces on the axis and related problems in the spaces of $(p,q)$-multipliers and their predual spaces”, Ural Math. J., 9:2 (2023), 4–27
V. V. Arestov, R. R. Akopyan, “Zadacha Stechkina o nailuchshem priblizhenii neogranichennogo operatora ogranichennymi i rodstvennye ei zadachi”, Tr. IMM UrO RAN, 26, no. 4, 2020, 7–31
Arestov V., “Uniform Approximation of Differentiation Operators By Bounded Linear Operators in the Spacel(R)”, Anal. Math., 46:3 (2020), 425–445
V. V. Arestov, “Best Uniform Approximation of the Differentiation Operator by Operators Bounded in the Space $L_2$”, Proc. Steklov Inst. Math. (Suppl.), 308, suppl. 1 (2020), S9–S30
Vitalii Arestov, Maria Filatova, “Best approximation of the differentiation operator in the space L2 on the semiaxis”, Journal of Approximation Theory, 187 (2014), 65
V. V. Arestov, M. A. Filatova, “The best approximation of the differentiation operator by linear bounded operators in the space L 2 on the semiaxis”, Dokl. Math., 90:2 (2014), 592
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
V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126
V. N. Gabushin, “Inequalities between derivatives in $L_p$-metrics for $0<p\leqslant\infty$”, Math. USSR-Izv., 10:4 (1976), 823–844

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

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