Comptes Rendus
no. 2
Mathematical analysis
An extremal problem for polynomials

Presented by: Jean-Pierre Kahane

Kai-Uwe Schmidt1
1 Faculty of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106 Magdeburg, Germany
Comptes Rendus. Mathématique, Volume 352 (2014) no. 2, pp. 95-97.

We give a solution to an extremal problem for polynomials, which asks for complex numbers α0,…,αn 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 αk or −αk.

Nous donnons dans ce papier une solution à un problème extrémal sur les polynômes, qui est de trouver des nombres complexes α0,…,αn 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 ke coefficient αk ou −αk.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.12.011

Kai-Uwe Schmidt 1

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