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

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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]). The extremal polynomial is expressed in the form of some linear combination of Chebyshev polynomials of the second kind.

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Literature cited

  1. P. L. Chebyshev, “The theory of mechanisms known under the name of parallelograms,” in: Complete Collected Works [in Russian], Vol. II, Moscow-Leningrad (1947), pp. 23–51.

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  3. E. I. Zolotarev, “On a problem on minimal quantities,” in: Complete Collected Works [in Russian], No. 2, Leningrad (1932), pp. 130–166.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    É. M. Galeev

Authors
  1. É. M. Galeev
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Translated from Matematicheskie Zametki, Vol. 17, No. 1, pp. 13–20, January, 1975.

In conclusion, the author expresses his gratitude to V. M. Tikhomirov and S. B. Stechkin for their help and interest in this paper.

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Galeev, É.M. Zolotarev problem in the metric of L1([−1, 1]). Mathematical Notes of the Academy of Sciences of the USSR 17, 9–13 (1975). https://doi.org/10.1007/BF01093834

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  • DOI: https://doi.org/10.1007/BF01093834

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