no. 2
Mathematical analysis
An extremal problem for polynomials
[Un problème extrémal pour les polynômes]

Présenté par : Jean-Pierre Kahane

Schmidt, Kai-Uwe1
1 Faculty of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106 Magdeburg, Germany
Comptes Rendus. Mathématique, Tome 352 (2014) no. 2, pp. 95-97.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.12.011
Schmidt, Kai-Uwe 1

1 Faculty of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106 Magdeburg, Germany 
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Schmidt, Kai-Uwe. An extremal problem for polynomials. Comptes Rendus. Mathématique, Tome 352 (2014) no. 2, pp. 95-97. doi : 10.1016/j.crma.2013.12.011. http://www.numdam.org/articles/10.1016/j.crma.2013.12.011/

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