An extremal problem for polynomials

Kai-Uwe Schmidt

doi:10.1016/j.crma.2013.12.011

Mathematical analysis

An extremal problem for polynomials
[Un problème extrémal pour les polynômes]

Présenté par : Jean-Pierre Kahane

Kai-Uwe Schmidt ¹

¹ Faculty of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106 Magdeburg, Germany

Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 95-97.

Résumé
Abstract

Nous donnons dans ce papier une solution à un problème extrémal sur les polynômes, qui est de trouver des nombres complexes $α_{0}, \dots, α_{n}$ de module égal à 1 qui minimisent, sur le cercle unité, la plus grande borne supérieure de la norme pour tous les polynômes de degré n qui ont pour $k^{e}$ coefficient $α_{k}$ ou $- α_{k}$ .

We give a solution to an extremal problem for polynomials, which asks for complex numbers $α_{0}, \dots, α_{n}$ of unit magnitude that minimise the largest supremum norm on the unit circle for all polynomials of degree n whose k-th coefficient is either $α_{k}$ or $- α_{k}$ .

Reçu le : 2013-03-23
Accepté le : 2013-12-12
Publié le : 2013-12-31

DOI : 10.1016/j.crma.2013.12.011

Affiliations des auteurs :

Kai-Uwe Schmidt ¹

¹ Faculty of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106 Magdeburg, Germany

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     title = {An extremal problem for polynomials},
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Kai-Uwe Schmidt. An extremal problem for polynomials. Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 95-97. doi : 10.1016/j.crma.2013.12.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.12.011/

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