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Mat. Zametki, 1972, Volume 12, Issue 5, Pages 531–538 (Mi mz9913)  

This article is cited in 4 scientific papers (total in 4 papers)

The best approximation of the differentiation operator in the metric of $L_p$

V. N. Gabushin

Institute of Mathematics and Mechanics, Academy of Sciences of the USSR

Abstract: For Stechkin's problem of the best approximation for the differentiation operator
$$ E_n=\inf_{\substack{L_q||V||_{L_p}\leqslant n}}\sup_{||f^{(l)}||_{L_r(S)}\leqslant 1}||f^{(k)}-Vf||_{L_q(S)} $$
we indicate the necessary and sufficient conditions that $E_n$ be finite. We study some properties of continuous linear operators $V$ from $L_p$ into $L_q$.

Full text: PDF file (850 kB)

English version:
Mathematical Notes, 1972, 12:5, 756–760

Bibliographic databases:

UDC: 517.4
Received: 20.09.1971

Citation: V. N. Gabushin, “The best approximation of the differentiation operator in the metric of $L_p$”, Mat. Zametki, 12:5 (1972), 531–538; Math. Notes, 12:5 (1972), 756–760

Citation in format AMSBIB
\Bibitem{Gab72}
\by V.~N.~Gabushin
\paper The best approximation of the differentiation operator in the metric of~$L_p$
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 5
\pages 531--538
\mathnet{http://mi.mathnet.ru/mz9913}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=324277}
\zmath{https://zbmath.org/?q=an:0262.41018}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 5
\pages 756--760
\crossref{https://doi.org/10.1007/BF01099059}


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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. V. N. Gabushin, “Inequalities between derivatives in $L_p$-metrics for $0<p\leqslant\infty$”, Math. USSR-Izv., 10:4 (1976), 823–844  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
    3. V. V. Arestov, M. A. Filatova, “On the approximation of the differentiation operator by linear bounded operators on the class of twice differentiable functions in the space $L_2(0,\infty)$”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 24–40  mathnet  crossref  isi  elib
    4. V. V. Arestov, “Nailuchshee ravnomernoe priblizhenie operatora differentsirovaniya ogranichennymi v prostranstve $L_2$ operatorami”, Tr. IMM UrO RAN, 24, no. 4, 2018, 34–56  mathnet  crossref  elib
  • Математические заметки Mathematical Notes
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