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Mat. Zametki, 1970, Volume 7, Issue 1, Pages 43–52 (Mi mz6991)  

This article is cited in 6 scientific papers (total in 7 papers)

Diameter of class $W^rL$ in $L(0,2\pi)$ and spline function approximation

Yu. N. Subbotin

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

Abstract: The $(2n-1)$-dimensional diameter of the class $W^rL$ is found in the metric of the space $L(0,2\pi)$. The rate of convergence is also studied of the interpolating spline functions $S_r(x,h)$ with equidistant nodes to a function $F(x)$ which has a uniformly continuous $k$-th derivative $(r\ge k\ge0)$ on the entire axis.

Full text: PDF file (563 kB)

English version:
Mathematical Notes, 1970, 7:1, 27–32

Bibliographic databases:

UDC: 517.5
Received: 21.07.1969

Citation: Yu. N. Subbotin, “Diameter of class $W^rL$ in $L(0,2\pi)$ and spline function approximation”, Mat. Zametki, 7:1 (1970), 43–52; Math. Notes, 7:1 (1970), 27–32

Citation in format AMSBIB
\Bibitem{Sub70}
\by Yu.~N.~Subbotin
\paper Diameter of class $W^rL$ in $L(0,2\pi)$ and spline function approximation
\jour Mat. Zametki
\yr 1970
\vol 7
\issue 1
\pages 43--52
\mathnet{http://mi.mathnet.ru/mz6991}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=259440}
\zmath{https://zbmath.org/?q=an:0198.09002|0195.07102}
\transl
\jour Math. Notes
\yr 1970
\vol 7
\issue 1
\pages 27--32
\crossref{https://doi.org/10.1007/BF01093337}


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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, “On extremal problems in the theory of best approximation”, Russian Math. Surveys, 29:3 (1974), 7–43  mathnet  crossref  mathscinet  zmath
    2. V. F. Babenko, N. V. Parfinovich, “Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency 2”, Math. Notes, 85:4 (2009), 515–527  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. F. Babenko, N. V. Parfinovich, “On the Exact Values of the Best Approximations of Classes of Differentiable Periodic Functions by Splines”, Math. Notes, 87:5 (2010), 623–635  mathnet  crossref  crossref  mathscinet  isi
    4. “Yurii Nikolaevich Subbotin. (K semidesyatipyatiletiyu so dnya rozhdeniya)”, Tr. IMM UrO RAN, 17, no. 3, 2011, 8–13  mathnet
    5. G. A. Akishev, “Estimates for Kolmogorov widths of the Nikol'skii — Besov — Amanov classes in the Lorentz space”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 1–12  mathnet  crossref  mathscinet  isi  elib
    6. Parfinovych N.V., “Exact Values of the Best (Oe > 1/4, Beta)-Approximations For the Classes of Convolutions With Kernels That Do Not Increase the Number of Sign Changes”, Ukr. Math. J., 69:8 (2018), 1248–1261  crossref  isi
    7. O. L. Vinogradov, “Analogi tozhdestva Rissa i tochnye neravenstva dlya proizvodnykh i raznostei splainov v integralnoi metrike”, Issledovaniya po lineinym operatoram i teorii funktsii. 47, Zap. nauchn. sem. POMI, 480, POMI, SPb., 2019, 86–102  mathnet
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