RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 6 scientific papers (total in 6 papers)

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.

Full text: PDF file (508 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 517.5
MSC: 42B99
Received: 14.02.1980

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}


Linking options:
  • http://mi.mathnet.ru/eng/msb2778
  • http://mi.mathnet.ru/eng/msb/v155/i1/p65

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath
    3. V. N. Temlyakov, “Approximation of periodic functions of several variables by bilinear forms”, Math. USSR-Izv., 28:1 (1987), 133–150  mathnet  crossref  mathscinet  zmath
    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    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  mathnet  zmath
    6. Temlyakov V., “on the Entropy Numbers of the Mixed Smoothness Function Classes”, J. Approx. Theory, 217 (2017), 26–56  crossref  mathscinet  zmath  isi  elib  scopus
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:334
    Full text:122
    References:34
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019