Comptes Rendus
Mathematical Analysis
A mapping connected with the Schur–Szegő composition
Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1355-1360.

Every monic polynomial in one variable of the form (x+1)S, degS=n1, is presentable in a unique way as a Schur–Szegő composition of n1 polynomials of the form (x+1)n1(x+ai). We prove geometric properties of the affine mapping associating to the coefficients of S the (n1)-tuple of values of the elementary symmetric functions of the numbers ai.

Tout polynôme unitaire à une variable de la forme (x+1)S, degS=n1, est présentable de façon unique comme composition de Schur–Szegő de n1 polynômes (x+1)n1(x+ai). Nous prouvons des propriétés géométriques de l'application affine associant aux coefficients de S le (n1)-uplet des valeurs des fonctions symétriques élémentaires des nombres ai.

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Published online:
DOI: 10.1016/j.crma.2009.10.025
Vladimir Petrov Kostov 1

1 Université de Nice, Laboratoire de Mathématiques, UMR 6621, parc Valrose, 06108 Nice cedex 2, France
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Vladimir Petrov Kostov. A mapping connected with the Schur–Szegő composition. Comptes Rendus. Mathématique, Volume 347 (2009) no. 23-24, pp. 1355-1360. doi : 10.1016/j.crma.2009.10.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.025/

[1] S. Alkhatib; V.P. Kostov The Schur–Szegő composition of real polynomials of degree 2, Rev. Mat. Complut., Volume 21 (2008), pp. 191-206

[2] V.P. Kostov The Schur–Szegő composition for hyperbolic polynomials, C. R. Acad. Sci. Paris Sér. I, Volume 345 (2007), pp. 483-488

[3] V.P. Kostov Eigenvectors in the context of the Schur–Szegő composition of polynomials, Math. Balkanica, Volume 22 (2008) no. 1–2, pp. 155-173

[4] V.P. Kostov; B.Z. Shapiro On the Schur–Szegő composition of polynomials, C. R. Acad. Sci. Paris Sér. I, Volume 343 (2006), pp. 81-86

[5] Victor Prasolov Polynomials, Algorithms and Computation in Mathematics, vol. 11, Springer-Verlag, Berlin, 2004

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