V. N. Gabushin, “On the best approximation of the differentiation operator on the half-line”, Mat. Zametki, 6:5 (1969), 573–582; Math. Notes, 6:5 (1969), 804

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Matematicheskie Zametki, 1969, Volume 6, Issue 5, Pages 573–582 (Mi mzm6965)

This article is cited in 17 scientific papers (total in 17 papers)

On the best approximation of the differentiation operator on the half-line

V. N. Gabushin

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

Full-text PDF (547 kB) Citations (17)

Abstract: We solve a problem of S. B. Stechkin concerning the best approximation in the metric of

C

$C$ to the operator of

k

$k$ -th order differentiation on certain classes of differentiable functions defined on the half-line, by linear operators whose norms from

L_{2}

$L_2$ into

C

$C$ are bounded. We consider the analogous problem for linear differential operators with constant coefficients.

Received: 06.01.1969

English version:
Mathematical Notes, 1969, Volume 6, Issue 5, Pages 804–810
DOI: https://doi.org/10.1007/BF01101408

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: V. N. Gabushin, “On the best approximation of the differentiation operator on the half-line”, Mat. Zametki, 6:5 (1969), 573–582; Math. Notes, 6:5 (1969), 804–810

Citation in format AMSBIB

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\by V.~N.~Gabushin

\paper On the best approximation of the differentiation operator on the half-line

\jour Mat. Zametki

\yr 1969

\vol 6

\issue 5

\pages 573--582

\mathnet{http://mi.mathnet.ru/mzm6965}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=259442}

\zmath{https://zbmath.org/?q=an:0216.13603}

\transl

\jour Math. Notes

\yr 1969

\vol 6

\issue 5

\pages 804--810

\crossref{https://doi.org/10.1007/BF01101408}

Linking options:

https://www.mathnet.ru/eng/mzm6965

https://www.mathnet.ru/eng/mzm/v6/i5/p573

This publication is cited in the following 17 articles:

Dmytro Skorokhodov, “The Landau–Kolmogorov problem on a finite interval in the Taikov case”, Journal of Approximation Theory, 280 (2022), 105771
Babenko V. Babenko Yu. Kriachko N. Skorokhodov D., “On Hardy-Littlewood-Polya and Taikov Type Inequalities For Multiple Operators in Hilbert Spaces”, Anal. Math., 47:4 (2021), 709–745
Kozynenko O. Skorokhodov D., “Kolmogorov-Type Inequalities For the Norms of Fractional Derivatives of Functions Defined on the Positive Half Line”, Ukr. Math. J., 72:10 (2021), 1579–1594
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
Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015), 20–29
S. V. Zelik, A. A. Ilyin, “Green's function asymptotics and sharp interpolation inequalities”, Russian Math. Surveys, 69:2 (2014), 209–260
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
A. R. Aliev, “On the Solvability of Initial Boundary-Value Problems for a Class of Operator-Differential Equations of Third Order”, Math. Notes, 90:3 (2011), 307–321
V. Tikhomirov, A. Kochurov, “Kolmogorov-type inequalities on the whole line or half line and the Lagrange principle in the theory of extremum problems”, Eurasian Math. J., 2:3 (2011), 125–142
S. S. Mirzoev, S. G. Veliev, “On the estimation of the norms of intermediate derivatives in some abstract spaces”, Zhurn. matem. fiz., anal., geom., 6:1 (2010), 73–83
A. A. Lunev, L. L. Oridoroga, “Exact Constants in Generalized Inequalities for Intermediate Derivatives”, Math. Notes, 85:5 (2009), 703–711
K. Watanabe, Y. Kametaka, A. Nagai, K. Takemura, H. Yamagishi, “The best constant of Sobolev inequality on a bounded interval”, Journal of Mathematical Analysis and Applications, 340:1 (2008), 699
G. A. Kalyabin, “Some Problems for Sobolev Spaces on the Half-line”, Proc. Steklov Inst. Math., 255 (2006), 150–158
G. A. Kalyabin, “Effective Formulas for Constants in the Stechkin–Gabushin Problem”, Proc. Steklov Inst. Math., 248 (2005), 118–124
G. A. Kalyabin, “Sharp Constants in Inequalities for Intermediate Derivatives (the Gabushin Case)”, Funct. Anal. Appl., 38:3 (2004), 184–191
G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Kolmogorov-type inequalities for derivatives”, Sb. Math., 188:12 (1997), 1799–1832
V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126

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

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