Algebraic polynomials least deviating from zero in measure on a segment

• Date: 2010
• Main Authors: Arestov, V. V., Арестов, B. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2868
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 anal...