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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






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


Tr. Mat. Inst. Steklova, 2014, Volume 284, Pages 8–37 (Mi tm3533)  

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

Nonlinear approximations of classes of periodic functions of many variables

D. B. Bazarkhanov

Institute of Mathematics, Almaty, Kazakhstan

Abstract: Order-sharp estimates are established for the best $N$-term approximations of functions in the classes $\mathrm B^{sm}_{pq}(\mathbb T^k)$ and $\mathrm L^{sm}_{pq}(\mathbb T^k)$ of Nikol'skii–Besov and Lizorkin–Triebel types with respect to the multiple system $\widetilde {\mathcal W}^m$ of Meyer wavelets in the metric of $L_r(\mathbb T^k)$ for various relations between the parameters $s,p,q,r$, and $m$ ($s=(s_1,…,s_n)\in\mathbb R^n_+$, $1\leq p,q,r\leq\infty$, $m=(m_1,…,m_n)\in\mathbb N^n$, and $k=m_1+…+m_n$). The proof of upper estimates is based on variants of the so-called greedy algorithms.

DOI: https://doi.org/10.1134/S0371968514010026

Full text: PDF file (387 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 284, 2–31

Bibliographic databases:

UDC: 517.518.8
Received in April 2013

Citation: D. B. Bazarkhanov, “Nonlinear approximations of classes of periodic functions of many variables”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Tr. Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 8–37; Proc. Steklov Inst. Math., 284 (2014), 2–31

Citation in format AMSBIB
\Bibitem{Baz14}
\by D.~B.~Bazarkhanov
\paper Nonlinear approximations of classes of periodic functions of many variables
\inbook Function spaces and related problems of analysis
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 284
\pages 8--37
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3533}
\crossref{https://doi.org/10.1134/S0371968514010026}
\elib{https://elibrary.ru/item.asp?id=21249100}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2014
\vol 284
\pages 2--31
\crossref{https://doi.org/10.1134/S0081543814010027}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000335559000001}
\elib{https://elibrary.ru/item.asp?id=27832582}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899814244}


Linking options:
  • http://mi.mathnet.ru/eng/tm3533
  • https://doi.org/10.1134/S0371968514010026
  • http://mi.mathnet.ru/eng/tm/v284/p8

    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. Sh. A. Balgimbayeva, “Nonlinear approximation of function spaces of mixed smoothness”, Siberian Math. J., 56:2 (2015), 262–274  mathnet  crossref  mathscinet  isi  elib
    2. D. B. Bazarkhanov, “Nonlinear trigonometric approximations of multivariate function classes”, Proc. Steklov Inst. Math., 293 (2016), 2–36  mathnet  crossref  crossref  mathscinet  isi  elib
    3. S. Balgimbayeva, T. Smirnov, “Nonlinear wavelet approximation of periodic function classes with generalized mixed smoothnes”, Anal. Math., 43:1 (2017), 1–26  crossref  mathscinet  zmath  isi  scopus
    4. D. B. Bazarkhanov, “Sparse approximation of some function classes with respect to multiple Haar system on the unit cube”, International conference functional analysis in interdisciplinary applications (FAIA 2017), AIP Conf. Proc., 1880, ed. T. Kalmenov, M. Sadybekov, Amer. Inst. Phys., 2017, UNSP 030017  crossref  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:332
    Full text:48
    References:98

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021