Hyperbolicity preservers and majorization

Julius Borcea; Petter Brändén

doi:10.1016/j.crma.2010.07.006

Mathematical Analysis

Hyperbolicity preservers and majorization
[Préservateurs d'hyperbolicité et majorisation]

Présenté par : Jean-Pierre Kahane

Julius Borcea ¹ ; Petter Brändén ¹

¹ Department of Mathematics, Stockholm University, 10691 Sweden

Comptes Rendus. Mathématique, Volume 348 (2010) no. 15-16, pp. 843-846.

Résumé
Abstract

L'ordre de majorisation de $R^{n}$ 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 $R^{n}$ 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 : 2010-06-07
Accepté le : 2010-07-08
Publié le : 2010-07-29

DOI : 10.1016/j.crma.2010.07.006

Affiliations des auteurs :

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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Felipe Rincón; Cynthia Vinzant; Josephine Yu Positively hyperbolic varieties, tropicalization, and positroids, Advances in Mathematics, Volume 383 (2021), p. 35 (Id/No 107677) | DOI:10.1016/j.aim.2021.107677 | Zbl:1471.14130
Mohan Ravichandran Principal Submatrices, Restricted Invertibility, and a Quantitative Gauss–Lucas Theorem, International Mathematics Research Notices, Volume 2020 (2020) no. 15, p. 4809 | DOI:10.1093/imrn/rny163

Cité par 2 documents. Sources : Crossref, zbMATH

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