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Algebraic polynomials least deviating from zero in measure on a segment

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Ukrainian Mathematical Journal Aims and scope

We investigate the problem of algebraic polynomials with given leading coefficients that deviate least from zero on the segment [–1, 1] with respect to a measure, or, more precisely, with respect to the functional μ(f) = mes{x ∈ [–1, 1]: ∣f (x)∣ ≥ 1}. We also discuss an analogous problem with respect to the integral functionals ∫ 1–1 φ (∣f (x)∣) dx for functions φ that are defined, nonnegative, and nondecreasing on the semiaxis [0, +∞).

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Authors and Affiliations

  1. Ural State University, Ekaterinburg, Russia

    V. V. Arestov

  2. Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Division, Ekaterinburg, Russia

    V. V. Arestov

Authors
  1. V. V. Arestov
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Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 3, pp. 291–300, March, 2010.

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Arestov, V.V. Algebraic polynomials least deviating from zero in measure on a segment. Ukr Math J 62, 331–342 (2010). https://doi.org/10.1007/s11253-010-0357-z

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  • DOI: https://doi.org/10.1007/s11253-010-0357-z

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