2017
Том 69
№ 9

# Algebraic polynomials least deviating from zero in measure on a segment

Arestov V. V.

Abstract

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 $μ(f) = \text{mes}\left\{x ∈ [–1, 1]: ∣f (x)∣ ≥ 1 \right\}$. 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 $[0, +∞)$.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 3, pp 331-342.

Citation Example: Arestov V. V. Algebraic polynomials least deviating from zero in measure on a segment // Ukr. Mat. Zh. - 2010. - 62, № 3. - pp. 291–300.

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