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 Mat. Sb. (N.S.), 1980, Volume 111(153), Number 1, Pages 144–156 (Mi msb2497)

Approximation of functions of several variables, taking account of the growth of the coefficients of the approximating combinations

V. V. Napalkov

Abstract: It is proved that every continuous function defined on the $n$-dimensional rectangular parallelepiped $\{x=(x_1,…,x_n)\in\mathbf R^n:0\leqslant x_i\leqslant a_i, 1\leqslant i\leqslant n\}$ can be approximated by polynomials of the form $Q(x)=\sum^p_{|\alpha|=0}c_\alpha x^\alpha$, where $c_\alpha=\eta_\alpha M(\alpha)$, with $\sum^p_{|\alpha|=0}|\eta_\alpha|\leqslant1$. Here $M(\alpha)$ is an arbitrary positive function defined on the set of multi-indices, and $\lim_{|\alpha|\to\infty}\sqrt[|\alpha|]{M(\alpha)}=\infty$.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1981, 39:1, 133–143

Bibliographic databases:

UDC: 517.5
MSC: 41A10, 41A63

Citation: V. V. Napalkov, “Approximation of functions of several variables, taking account of the growth of the coefficients of the approximating combinations”, Mat. Sb. (N.S.), 111(153):1 (1980), 144–156; Math. USSR-Sb., 39:1 (1981), 133–143

Citation in format AMSBIB
\Bibitem{Nap80} \by V.~V.~Napalkov \paper Approximation of functions of several variables, taking account of the growth of the coefficients of the approximating combinations \jour Mat. Sb. (N.S.) \yr 1980 \vol 111(153) \issue 1 \pages 144--156 \mathnet{http://mi.mathnet.ru/msb2497} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=560468} \zmath{https://zbmath.org/?q=an:0462.41003|0438.41008} \transl \jour Math. USSR-Sb. \yr 1981 \vol 39 \issue 1 \pages 133--143 \crossref{https://doi.org/10.1070/SM1981v039n01ABEH001477} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981LQ97300007} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. I. F. Krasichkov-Ternovskii, “On absolute completeness of systems of exponentials on a closed interval”, Math. USSR-Sb., 59:2 (1988), 303–315
2. B. N. Khabibullin, “Stability of Completeness for Systems of Exponentials on Compact Convex Sets in $\mathbb C$”, Math. Notes, 72:4 (2002), 542–550
3. I. F. Krasichkov-Ternovskii, G. N. Shilova, “Absolute completeness of systems of exponentials on convex compact sets”, Sb. Math., 196:12 (2005), 1801–1814
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