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Mat. Zametki, 1969, Volume 6, Issue 5, Pages 573–582 (Mi mz6965)  

This article is cited in 12 scientific papers (total in 12 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

Abstract: We solve a problem of S. B. Stechkin concerning the best approximation in the metric of $C$ to the operator of $k$-th order differentiation on certain classes of differentiable functions defined on the half-line, by linear operators whose norms from $L_2$ into $C$ are bounded. We consider the analogous problem for linear differential operators with constant coefficients.

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English version:
Mathematical Notes, 1969, 6:5, 804–810

Bibliographic databases:

UDC: 517.5
Received: 06.01.1969

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
\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
\jour Math. Notes
\yr 1969
\vol 6
\issue 5
\pages 804--810

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    This publication is cited in the following articles:
    1. 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
    2. G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Kolmogorov-type inequalities for derivatives”, Sb. Math., 188:12 (1997), 1799–1832  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. G. A. Kalyabin, “Sharp Constants in Inequalities for Intermediate Derivatives (the Gabushin Case)”, Funct. Anal. Appl., 38:3 (2004), 184–191  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. G. A. Kalyabin, “Effective Formulas for Constants in the Stechkin–Gabushin Problem”, Proc. Steklov Inst. Math., 248 (2005), 118–124  mathnet  mathscinet  zmath
    5. G. A. Kalyabin, “Some Problems for Sobolev Spaces on the Half-line”, Proc. Steklov Inst. Math., 255 (2006), 150–158  mathnet  crossref  mathscinet  elib
    6. A. A. Lunev, L. L. Oridoroga, “Exact Constants in Generalized Inequalities for Intermediate Derivatives”, Math. Notes, 85:5 (2009), 703–711  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. 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  mathnet  mathscinet  zmath
    8. 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  mathnet  crossref  crossref  mathscinet  isi
    9. 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  mathnet  mathscinet  zmath
    10. S. V. Zelik, A. A. Ilyin, “Green's function asymptotics and sharp interpolation inequalities”, Russian Math. Surveys, 69:2 (2014), 209–260  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. 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
    12. Vitalii V. Arestov, “On the best approximation of the differentiation operator”, Ural Math. J., 1:1 (2015), 20–29  mathnet  crossref  zmath
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