Matematicheskie Zametki
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
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



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






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


Matematicheskie Zametki, 2009, Volume 85, Issue 4, Pages 538–551
DOI: https://doi.org/10.4213/mzm4617
(Mi mzm4617)
 

This article is cited in 5 scientific papers (total in 5 papers)

Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency 2

V. F. Babenkoab, N. V. Parfinovichb

a Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
b Dnepropetrovsk National University
Full-text PDF (569 kB) Citations (5)
References:
Abstract: We obtain exact values of best $L_1$-approximations for the classes $W^rF$, $r\in\mathbb N$, of periodic functions whose $r$th derivative belongs to a given rearrangement-invariant set $F$ as well as for the classes $W^rH^\omega$ of periodic functions whose $r$th derivative has a given convex (up) majorant $\omega(t)$ of the modulus of continuity by subspaces of polynomial splines of order $m\ge r+1$ of deficiency 2 with nodes at the points $2k\pi/n$, $n\in\mathbb N$, $k\in\mathbb Z$. It is shown that these subspaces are extremal for the Kolmogorov widths of the corresponding function classes.
Keywords: periodic function, best $L_1$-approximation, periodic function, polynomial spline of deficiency 2, Kolmogorov width, rearrangement-invariant set, modulus of continuity.
Received: 07.03.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 4, Pages 515–527
DOI: https://doi.org/10.1134/S0001434609030237
Bibliographic databases:
UDC: 517
Language: Russian
Citation: V. F. Babenko, N. V. Parfinovich, “Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency 2”, Mat. Zametki, 85:4 (2009), 538–551; Math. Notes, 85:4 (2009), 515–527
Citation in format AMSBIB
\Bibitem{BabPar09}
\by V.~F.~Babenko, N.~V.~Parfinovich
\paper Exact Values of Best Approximations for Classes of Periodic Functions by Splines of Deficiency~2
\jour Mat. Zametki
\yr 2009
\vol 85
\issue 4
\pages 538--551
\mathnet{http://mi.mathnet.ru/mzm4617}
\crossref{https://doi.org/10.4213/mzm4617}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2549416}
\zmath{https://zbmath.org/?q=an:05628181}
\transl
\jour Math. Notes
\yr 2009
\vol 85
\issue 4
\pages 515--527
\crossref{https://doi.org/10.1134/S0001434609030237}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000266561100023}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-69949121291}
Linking options:
  • https://www.mathnet.ru/eng/mzm4617
  • https://doi.org/10.4213/mzm4617
  • https://www.mathnet.ru/eng/mzm/v85/i4/p538
  • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:511
    Full-text PDF :210
    References:50
    First page:14
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024