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 Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 3, Pages 217–224 (Mi timm733)

The best $L_p$ approximation of the Laplace operator by linear bounded operators in the classes of functions of two and three variables

A. A. Koshelev

Ural Federal University

Abstract: Close two-sided estimates are obtained for the best approximation in the space $L_p(\mathbb R^m)$, $m=2,3$, $1\le p\le\infty$, of the Laplace operator by linear bounded operators in the class of functions for which the square of the Laplace operator belongs to the space $L_p(\mathbb R^m)$. We estimate the best constant in the corresponding Kolmogorov inequality and the error of the optimal recovery of the values of the Laplace operator on functions from this class given with an error. We write an operator whose deviation from the Laplace operator is close to the best.

Keywords: Laplace operator, approximation of unbounded operators by bounded operators, Kolmogorov inequality, optimal recovery.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, 277, suppl. 1, 136–144

Bibliographic databases:

UDC: 517.518

Citation: A. A. Koshelev, “The best $L_p$ approximation of the Laplace operator by linear bounded operators in the classes of functions of two and three variables”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 3, 2011, 217–224; Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 136–144

Citation in format AMSBIB
\Bibitem{Kos11} \by A.~A.~Koshelev \paper The best $L_p$ approximation of the Laplace operator by linear bounded operators in the classes of functions of two and three variables \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2011 \vol 17 \issue 3 \pages 217--224 \mathnet{http://mi.mathnet.ru/timm733} \elib{https://elibrary.ru/item.asp?id=17870133} \transl \jour Proc. Steklov Inst. Math. (Suppl.) \yr 2012 \vol 277 \issue , suppl. 1 \pages 136--144 \crossref{https://doi.org/10.1134/S0081543812050136} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305909000013} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84863566757} 

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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. A. A. Koshelev, “The Landau–Kolmogorov problem for the Laplace operator on a ball”, Russian Math. (Iz. VUZ), 60:2 (2016), 25–32
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