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Mat. Zametki, 1975, Volume 17, Issue 1, Pages 13–20 (Mi mz7218)  

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

Zolotarev problem in the metric of $L_1([-1,1])$

È. M. Galeev

M. V. Lomonosov Moscow State University, USSR

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 $L_1([-1,1])$. The extremal polynomial is expressed in the form of some linear combination of Chebyshev polynomials of the second kind.

Full text: PDF file (410 kB)

English version:
Mathematical Notes, 1975, 17:1, 9–13

Bibliographic databases:

UDC: 517.5
Received: 05.07.1974

Citation: È. M. Galeev, “Zolotarev problem in the metric of $L_1([-1,1])$”, 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/mz7218}
\mathscinet{http://www.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}


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    Remarks

    This publication is cited in the following articles:
    1. 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
    2. 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
    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. A. Yudin, “On Polynomials of Least Deviation from Zero”, Math. Notes, 87:5 (2010), 779–783  mathnet  crossref  crossref  mathscinet  isi
    5. 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
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