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






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


Mat. Zametki, 2004, Volume 76, Issue 2, Pages 216–225 (Mi mz101)  

Best Uniform Rational Approximations of Functions by Orthoprojections

A. A. Pekarskii

Belarusian State Technological University

Abstract: Let $C[-1,1]$ be the Banach space of continuous complex functions $f$ on the interval $[-1,1]$ equipped with the standard maximum norm $\|f\|$; let $\omega( \cdot )=\omega( \cdot ,f$ be the modulus of continuity of $f$; and let $R_n=R_n(f)$ be the best uniform approximation of $f$ by rational functions (r.f.) whose degrees do not exceed $n=1,2,\ldots$. The space $C[-1,1]$ is also regarded as a pre-Hilbert space with respect to the inner product given by $(f,g)=(1/\pi)\int_{-1}^1f(x)g(x)(1-x^2)^{-1/2} dx$. Let $z_n=ż_1,z_2,\ldots,z_n\}$ be a set of points located outside the interval $[-1,1]$. By $F( \cdot ,f,z_n)$ we denote an orthoprojection operator acting from the pre-Hilbert space $C[-1,1]$ onto its $(n+1)$-dimensional subspace consisting of rational functions whose poles (with multiplicity taken into account) can only be points of the set $z_n$. In this paper, we show that if $f$ is not a rational function of degree $\leqslant n$, then we can find a set of points $z_n=z_n(f)$ such that $\|f( \cdot )-F( \cdot ,f,z_n)\|\leqslant 12R_n\ln\frac3{\omega^{-1}(R_n/3)}$.

DOI: https://doi.org/10.4213/mzm101

Full text: PDF file (216 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2004, 76:2, 200–208

Bibliographic databases:

UDC: 517.53
Received: 06.05.2002

Citation: A. A. Pekarskii, “Best Uniform Rational Approximations of Functions by Orthoprojections”, Mat. Zametki, 76:2 (2004), 216–225; Math. Notes, 76:2 (2004), 200–208

Citation in format AMSBIB
\Bibitem{Pek04}
\by A.~A.~Pekarskii
\paper Best Uniform Rational Approximations of Functions by Orthoprojections
\jour Mat. Zametki
\yr 2004
\vol 76
\issue 2
\pages 216--225
\mathnet{http://mi.mathnet.ru/mz101}
\crossref{https://doi.org/10.4213/mzm101}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2098993}
\zmath{https://zbmath.org/?q=an:1059.41013}
\transl
\jour Math. Notes
\yr 2004
\vol 76
\issue 2
\pages 200--208
\crossref{https://doi.org/10.1023/B:MATN.0000036758.61603.90}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000223760500023}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-4043154810}


Linking options:
  • http://mi.mathnet.ru/eng/mz101
  • https://doi.org/10.4213/mzm101
  • http://mi.mathnet.ru/eng/mz/v76/i2/p216

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:193
    Full text:65
    References:23
    First page:2

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