2020/05/25 by Dmitriy Dmitrishin, Dmitrishin, Dmitriy, Andrey Smorodin +3 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.2005.12432
openalex publication_date 2020/05/25 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Extremal problems for typically real polynomials go back to a paper by W. W. Rogosinski and G. Szegő, where a number of problems were posed, which were partially solved by using orthogonal polynomials. Since then, not too many new results on extremal properties of typically real polynomials have been obtained. Fundamental work in this direction is due to M.~Brandt, who found a novel way of solving extremal problems. In particular, he solved C. Michel's problem of estimating the modulus of a typically real polynomial of odd degree. On the other hand, D. K. Dimitrov showed the effectivity of Fejér's method for solving the Rogosinski--Szegő problems. In this article, we completely solve Michel's problem by using Fejér's method.