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 Mat. Sb. (N.S.), 1980, Volume 113(155), Number 1(9), Pages 65–80 (Mi msb2778)

Approximation of periodic functions of several variables with bounded mixed difference

V. N. Temlyakov

Abstract: This paper studies questions concerning the approximation of functions of several variables by trigonometric polynomials whose harmonics lie in a “hyperbolic cross” and also properties of functions which do not have harmonics lying in a “hyperbolic cross”. Analogues of H. Bohr's inequality are obtained for such functions. Estimates of optimal order are obtained for the upper bounds of best approximations of certain classes of functions, defined using mixed differences, by trigonometric polynomials whose harmonics lie in a “hyperbolic cross”. The diameters of certain classes are found.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 41:1, 53–66

Bibliographic databases:

UDC: 517.5
MSC: 42B99

Citation: V. N. Temlyakov, “Approximation of periodic functions of several variables with bounded mixed difference”, Mat. Sb. (N.S.), 113(155):1(9) (1980), 65–80; Math. USSR-Sb., 41:1 (1982), 53–66

Citation in format AMSBIB
\Bibitem{Tem80} \by V.~N.~Temlyakov \paper Approximation of periodic functions of several variables with bounded mixed difference \jour Mat. Sb. (N.S.) \yr 1980 \vol 113(155) \issue 1(9) \pages 65--80 \mathnet{http://mi.mathnet.ru/msb2778} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=590538} \zmath{https://zbmath.org/?q=an:0479.42002|0455.42005} \transl \jour Math. USSR-Sb. \yr 1982 \vol 41 \issue 1 \pages 53--66 \crossref{https://doi.org/10.1070/SM1982v041n01ABEH002220} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980NC13900003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84921883677} 

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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. Temlyakov, “Approximation of functions with a bounded mixed difference by trigonometric polynomials, and the widths of some classes of functions”, Math. USSR-Izv., 20:1 (1983), 173–187
2. V. N. Temlyakov, “Approximation of periodic functions of several variables by trigonometric polynomials, and widths of some classes of functions”, Math. USSR-Izv., 27:2 (1986), 285–322
3. V. N. Temlyakov, “Approximation of periodic functions of several variables by bilinear forms”, Math. USSR-Izv., 28:1 (1987), 133–150
4. È. M. Galeev, “Order estimates of smallest norms, with respect to the choice of $N$ harmonics, of derivatives of the Dirichlet and Favard kernels”, Math. USSR-Sb., 72:2 (1992), 567–578
5. G. Akishev, “O poryadkakh priblizheniya klassov gladkikh funktsii v prostranstvakh Lebega so smeshannoi normoi”, Uchen. zap. Kazan. gos. un-ta. Ser. Fiz.-matem. nauki, 148, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2006, 5–17
6. Temlyakov V., “on the Entropy Numbers of the Mixed Smoothness Function Classes”, J. Approx. Theory, 217 (2017), 26–56
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