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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 


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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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).

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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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