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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 1, Pages 137–155 (Mi izv1474)  

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

Approximation of periodic functions of several variables by bilinear forms

V. N. Temlyakov


Abstract: The orders of the quantities
$$ \tau_M(F)_{p_1,p_2}=\sup_{f\in F}\inf_{\substack{u_i(\mathbf x),v_i(\mathbf y)
i=1,…,M}}\|f(\mathbf x-\mathbf y)-\sum_{i=1}^Mu_i(\mathbf x)v_i(\mathbf y)\|_{p_1,p_2} $$
are obtained, where $F$ is a class of functions with mixed derivative, or the corresponding prelimiting difference, bounded in $L_q$. In the process some results of independent interest are obtained: a generalization of the Hardy–Littlewood theorem, and the orders of the best $M$-term trigonometric approximations.
Bibliography: 16 titles.

Full text: PDF file (1760 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1987, 28:1, 133–150

Bibliographic databases:

UDC: 517.5
MSC: 42B05, 41A63, 41A17
Received: 24.02.1983

Citation: V. N. Temlyakov, “Approximation of periodic functions of several variables by bilinear forms”, Izv. Akad. Nauk SSSR Ser. Mat., 50:1 (1986), 137–155; Math. USSR-Izv., 28:1 (1987), 133–150

Citation in format AMSBIB
\Bibitem{Tem86}
\by V.~N.~Temlyakov
\paper Approximation of periodic functions of several variables by bilinear forms
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 1
\pages 137--155
\mathnet{http://mi.mathnet.ru/izv1474}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=835569}
\zmath{https://zbmath.org/?q=an:0651.42002|0607.42003}
\transl
\jour Math. USSR-Izv.
\yr 1987
\vol 28
\issue 1
\pages 133--150
\crossref{https://doi.org/10.1070/IM1987v028n01ABEH000870}


Linking options:
  • http://mi.mathnet.ru/eng/izv1474
  • http://mi.mathnet.ru/eng/izv/v50/i1/p137

    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. Jan Schneider, “Error estimates for two-dimensional cross approximation”, Journal of Approximation Theory, 162:9 (2010), 1685  crossref
    2. V. N. Temlyakov, “Constructive sparse trigonometric approximation and other problems for functions with mixed smoothness”, Sb. Math., 206:11 (2015), 1628–1656  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Temlyakov V., “Sparse Approximation by Greedy Algorithms”, Mathematical Analysis, Probability and Applications – Plenary Lectures, Springer Proceedings in Mathematics & Statistics, Springer Proceedings in Mathematics & Statistics, 177, ed. Qian T. Rodino L., Springer, 2016, 183–215  crossref  mathscinet  isi  scopus
    4. Temlyakov V., “Constructive Sparse Trigonometric Approximation For Functions With Small Mixed Smoothness”, Constr. Approx., 45:3 (2017), 467–495  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:375
    Full text:136
    References:46
    First page:2

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