Algebraic polynomials least deviating from zero in measure on a segment - Arestov, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
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, +∞).