We give a solution of the problem on trigonometric polynomials f n with the given leading harmonic y cos nt that deviate the least from zero in measure, more precisely, with respect to the functional µ( f n ) = mes{t ∈ [0, 2π] : | f n (t)| ≥ 1}. For trigonometric polynomials with a fixed leading harmonic, we consider the least uniform deviation from zero on a compact set and find the minimal value of the deviation over compact subsets of the torus that have a given measure. We give a solution of a similar problem on the unit circle for algebraic polynomials with zeros on the circle.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.