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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 2, Pages 266–290 (Mi izv1557)  

This article is cited in 2 scientific papers (total in 2 papers)

Widths in $L_p$ of classes of continuous and of differentiable functions, and optimal methods of coding and recovering functions and their derivatives

N. P. Korneichuk


Abstract: Exact values of linear widths (diameters), Kolmogorov widths and Gel'fand widths, in $L_p$-spaces are found for some classes of functions, using a convex majorant of the modulus of continuity of a function or its derivative. Precise constants in the Jackson type theorems on approximation of continuous and differentiable functions are also found. These results are interpreted from the point of view of problems of optimal coding and optimal recovery of functions and their derivatives.
Bibliography: 23 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1982, 18:2, 227–247

Bibliographic databases:

UDC: 517.5
MSC: Primary 41A65; Secondary 41A17, 41A50
Received: 21.04.1980

Citation: N. P. Korneichuk, “Widths in $L_p$ of classes of continuous and of differentiable functions, and optimal methods of coding and recovering functions and their derivatives”, Izv. Akad. Nauk SSSR Ser. Mat., 45:2 (1981), 266–290; Math. USSR-Izv., 18:2 (1982), 227–247

Citation in format AMSBIB
\Bibitem{Kor81}
\by N.~P.~Korneichuk
\paper Widths in $L_p$ of classes of continuous and of differentiable functions, and optimal methods of coding and recovering functions and their derivatives
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 2
\pages 266--290
\mathnet{http://mi.mathnet.ru/izv1557}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=616223}
\zmath{https://zbmath.org/?q=an:0536.41026|0511.41030}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 18
\issue 2
\pages 227--247
\crossref{https://doi.org/10.1070/IM1982v018n02ABEH001387}


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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. N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. Erich Novak, “Quadrature and widths”, Journal of Approximation Theory, 47:3 (1986), 195  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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