no. 11
Mathematical Analysis
Matrix-theoretical derivations of some results of Borcea–Shapiro on hyperbolic polynomials
[La dérivation matricielle de certaines résultats de Borcea–Shapiro sur les polynômes hyperboliques]

Présenté par : Jean-Pierre Kahane

Pereira, Rajesh1
1 Department of Mathematics and Statistics, University of Saskatchewan, S7N 5E6 Saskatoon SK, Canada
Comptes Rendus. Mathématique, Tome 341 (2005) no. 11, pp. 651-653.

On utilise l'analyse matricielle pour obtenir des démonstrations simples de deux résultats de Borcea–Shapiro sur la relation de majoration entre certains polynômes hyperboliques. On obtient aussi un résultat apparenté sur la majoration des zéros de polynômes complexes.

We use matrix analysis to give simple proofs of two theorems of Borcea–Shapiro which yield majorization relations between certain hyperbolic polynomials. We also prove a conjecture of Borcea involving majorization and the zeros of polynomials.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.10.002
Pereira, Rajesh 1

1 Department of Mathematics and Statistics, University of Saskatchewan, S7N 5E6 Saskatoon SK, Canada 
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Pereira, Rajesh. Matrix-theoretical derivations of some results of Borcea–Shapiro on hyperbolic polynomials. Comptes Rendus. Mathématique, Tome 341 (2005) no. 11, pp. 651-653. doi : 10.1016/j.crma.2005.10.002. http://www.numdam.org/articles/10.1016/j.crma.2005.10.002/

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