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Comptes Rendus Mathématique
Volume 345, n° 9
pages 483-488 (novembre 2007)
Doi : 10.1016/j.crma.2007.10.003
Received : 11 April 2007 ;  accepted : 28 September 2007
The Schur-Szegö composition for hyperbolic polynomials
La composition de Schur-Szegö de polynômes hyperboliques
 

Vladimir Petrov Kostov
Laboratoire J.-A. Dieudonné, UMR 6621 du CNRS, Université de Nice, parc Valrose, 06108 Nice cedex 2, France 

Abstract

The composition of Schur-Szegö of the polynomials   and   is defined as  . In the case when P and Q are hyperbolic, i.e. with real roots only, we give the exhaustive answer to the question if the numbers of positive, negative and zero roots of P and Q are known what these numbers can be for  . To cite this article: V.P. Kostov, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The full text of this article is available in PDF format.
Résumé

La composition de Schur-Szegö des polynômes   et   est définie comme  . Dans le cas où P et Q sont hyperboliques, c. à d. nʼayant que des racines réelles, nous donnons la réponse exhaustive à la question si on connaît les nombres de racines positives, négatives et nulles de P et Q , quels peuvent être ces nombres pour  . Pour citer cet article : V.P. Kostov, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

The full text of this article is available in PDF format.

 Research partially supported by Wenner-Grenn Foundation.



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