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Comptes Rendus Mathématique
Volume 348, n° 15-16
pages 843-846 (août 2010)
Doi : 10.1016/j.crma.2010.07.006
Received : 7 June 2010 ;  accepted : 8 July 2010
Hyperbolicity preservers and majorization
Préservateurs d'hyperbolicité et majorisation
 

Julius Borcea, Petter Brändén 1
Department of Mathematics, Stockholm University, 10691 Sweden 

Abstract

The majorization order on   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.

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Résumé

L'ordre de majorisation de   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 full text of this article is available in PDF format.
1  The author is a Royal Swedish Academy of Sciences Research Fellow supported by a grant from the Knut and Alice Wallenberg Foundation.


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