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Matematicheskie Zametki, 1975, Volume 17, Issue 1, Pages 13–20 (Mi mzm7218)  
This article is cited in 7 scientific papers (total in 7 papers)

Zolotarev problem in the metric of L1([−1,1])L1([−1,1])

È. M. Galeev

M. V. Lomonosov Moscow State University, USSR
Full-text PDF (410 kB) Citations (7)
Abstract: In this paper we solve the problem of the determination of a polynomial of degree n with given two leading coefficients which has the least deviation from zero in the metric of L1([−1,1])L1([−1,1]). The extremal polynomial is expressed in the form of some linear combination of Chebyshev polynomials of the second kind.
Received: 05.07.1974
English version:
Mathematical Notes, 1975, Volume 17, Issue 1, Pages 9–13
DOI: https://doi.org/10.1007/BF01093834
Bibliographic databases:
UDC: 517.5
Language: Russian
Citation: È. M. Galeev, “Zolotarev problem in the metric of L1([−1,1])L1([−1,1])”, Mat. Zametki, 17:1 (1975), 13–20; Math. Notes, 17:1 (1975), 9–13
Citation in format AMSBIB
\Bibitem{Gal75}
\by \`E.~M.~Galeev
\paper Zolotarev problem in the metric of $L_1([-1,1])$
\jour Mat. Zametki
\yr 1975
\vol 17
\issue 1
\pages 13--20
\mathnet{http://mi.mathnet.ru/mzm7218}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=361566}
\zmath{https://zbmath.org/?q=an:0321.41019|0315.41024}
\transl
\jour Math. Notes
\yr 1975
\vol 17
\issue 1
\pages 9--13
\crossref{https://doi.org/10.1007/BF01093834}
Linking options:
  • https://www.mathnet.ru/eng/mzm7218
  • https://www.mathnet.ru/eng/mzm/v17/i1/p13
    Remarks
    This publication is cited in the following 7 articles:
    1. V. A. Yudin, “On Polynomials of Least Deviation from Zero”, Math. Notes, 87:5 (2010), 779–783  mathnet  crossref  crossref  mathscinet  isi
    2. A. G. Babenko, Yu. V. Kryakin, V. A. Yudin, “On one of Geronimus's results”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S37–S48  mathnet  crossref  isi  elib
    3. A. G. Babenko, Yu. V. Kryakin, “Integral approximation of the characteristic function of an interval by trigonometric polynomials”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S19–S38  mathnet  crossref  isi  elib
    4. V. E. Geit, “O polinomakh, naimenee uklonyayuschikhsya ot nulya v metrike $L[-1,1]$ (vtoroe soobschenie)”, Sib. zhurn. vychisl. matem., 4:2 (2001), 123–136  mathnet  zmath
    5. V. E. Geit, “O polinomakh, naimenee uklonyayuschikhsya ot nulya v metrike $L[-1,1]$”, Sib. zhurn. vychisl. matem., 2:3 (1999), 223–238  mathnet  zmath
    6. Franz Peherstorfer, “Trigonometric polynomial approximation in theL 1-norm”, Math Z, 169:3 (1979), 261  crossref
    7. Franz Peherstorfer, Paul Otto Runck, Linear Spaces and Approximation / Lineare Räume und Approximation, 1978, 423  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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