V. Markov's problem for monotone polynomials

2012/05/04 by Oleksiy Klurman, Klurman, Oleksiy
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1205.0846

arxiv created 2012/05/04 · arxiv updated 2012/05/07

Abstract

We consider the classical problem of estimating norm of the derivative of algebraic polynomial via the norm of polynomial itself. The corresponding extremal problem for general polynomials in uniform norm was solved by V. Markov. In this note we solve analogous problem for monotone polynomials. As a consequence, we find exact constant in Bernstein inequality for monotone polynomials.

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