Comptes Rendus
no. 15-16
Mathematical Analysis
Hyperbolicity preservers and majorization
[Préservateurs d'hyperbolicité et majorisation]

Présenté par : Jean-Pierre Kahane

Julius Borcea1 ; Petter Brändén1
1 Department of Mathematics, Stockholm University, 10691 Sweden
Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 843-846.

L'ordre de majorisation de Rn induit un ordre partiel naturel sur l'espace des polynômes hyperboliques univariés de degré n. Nous caractérisons les opérateurs linéaires sur ces polynômes préservant l'ordre donné et montrons que seule la préservation de l'hyperbolicité suffit (modulo des contraintes évidentes sur le degré).

The majorization order on Rn induces a natural partial ordering on the space of univariate hyperbolic polynomials of degree n. We characterize all linear operators on polynomials that preserve majorization, and show that it is sufficient (modulo obvious degree constraints) to preserve hyperbolicity.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.07.006
Julius Borcea 1 ; Petter Brändén 1

1 Department of Mathematics, Stockholm University, 10691 Sweden 
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Julius Borcea; Petter Brändén. Hyperbolicity preservers and majorization. Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 843-846. doi : 10.1016/j.crma.2010.07.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.07.006/

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