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Mat. Zametki, 1975, Volume 18, Issue 1, Pages 97–108 (Mi mz7630)  

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

Linear deviations of the classes $\widetilde W_p^\alpha$ and approximations in spaces of multipliers

B. E. Klots

State Scientific Research Energy Institute

Abstract: We consider the problem of the asymptotically best linear method of approximation in the metric of $L_s[-\pi,\pi]$ of the set $\widetilde W_p^\alpha(1)$ of periodic functions with a bounded in $L_p[-\pi,\pi]$ fractional derivative, by functions from $\widetilde W_p^\beta(M)$ ,beta >agr, for sufficiently large M, and the problem about the best approximation in $L_s[-\pi,\pi]$ of the operator of differentiation on $\widetilde W_p^\alpha(1)$ by continuous linear operators whose norm (as operators from $L_r[-\pi,\pi]$ into $L_q[-\pi,\pi]$)does not exceed $M$. These problems are reduced to the approximation of an individual element in the space of multipliers, and this allows us to obtain estimates that are exact in the sense of the order.

Full text: PDF file (747 kB)

English version:
Mathematical Notes, 1975, 18:1, 640–646

Bibliographic databases:

UDC: 517.5
Received: 10.01.1974

Citation: B. E. Klots, “Linear deviations of the classes $\widetilde W_p^\alpha$ and approximations in spaces of multipliers”, Mat. Zametki, 18:1 (1975), 97–108; Math. Notes, 18:1 (1975), 640–646

Citation in format AMSBIB
\Bibitem{Klo75}
\by B.~E.~Klots
\paper Linear deviations of the classes $\widetilde W_p^\alpha$ and approximations in spaces of multipliers
\jour Mat. Zametki
\yr 1975
\vol 18
\issue 1
\pages 97--108
\mathnet{http://mi.mathnet.ru/mz7630}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=390600}
\zmath{https://zbmath.org/?q=an:0329.41023}
\transl
\jour Math. Notes
\yr 1975
\vol 18
\issue 1
\pages 640--646
\crossref{https://doi.org/10.1007/BF01461146}


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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. B. E. Klots, “Best linear and nonlinear approximations for smooth functions”, Funct. Anal. Appl., 12:1 (1978), 12–19  mathnet  crossref  mathscinet  zmath
    2. 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
  • Математические заметки Mathematical Notes
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