Every monic polynomial in one variable of the form , , is presentable in a unique way as a Schur–Szegő composition of polynomials of the form . We prove geometric properties of the affine mapping associating to the coefficients of S the -tuple of values of the elementary symmetric functions of the numbers .
Tout polynôme unitaire à une variable de la forme , , est présentable de façon unique comme composition de Schur–Szegő de polynômes . Nous prouvons des propriétés géométriques de l'application affine associant aux coefficients de S le -uplet des valeurs des fonctions symétriques élémentaires des nombres .
Accepted:
Published online:
@article{CRMATH_2009__347_23-24_1355_0, author = {Kostov, Vladimir Petrov}, title = {A mapping connected with the {Schur{\textendash}Szeg\H{o}} composition}, journal = {Comptes Rendus. Math\'ematique}, pages = {1355--1360}, publisher = {Elsevier}, volume = {347}, number = {23-24}, year = {2009}, doi = {10.1016/j.crma.2009.10.025}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2009.10.025/} }
TY - JOUR AU - Kostov, Vladimir Petrov TI - A mapping connected with the Schur–Szegő composition JO - Comptes Rendus. Mathématique PY - 2009 SP - 1355 EP - 1360 VL - 347 IS - 23-24 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.10.025/ DO - 10.1016/j.crma.2009.10.025 LA - en ID - CRMATH_2009__347_23-24_1355_0 ER -
%0 Journal Article %A Kostov, Vladimir Petrov %T A mapping connected with the Schur–Szegő composition %J Comptes Rendus. Mathématique %D 2009 %P 1355-1360 %V 347 %N 23-24 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.10.025/ %R 10.1016/j.crma.2009.10.025 %G en %F CRMATH_2009__347_23-24_1355_0
Kostov, Vladimir Petrov. 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. http://www.numdam.org/articles/10.1016/j.crma.2009.10.025/
[1] The Schur–Szegő composition of real polynomials of degree 2, Rev. Mat. Complut., Volume 21 (2008), pp. 191-206
[2] The Schur–Szegő composition for hyperbolic polynomials, C. R. Acad. Sci. Paris Sér. I, Volume 345 (2007), pp. 483-488
[3] Eigenvectors in the context of the Schur–Szegő composition of polynomials, Math. Balkanica, Volume 22 (2008) no. 1–2, pp. 155-173
[4] On the Schur–Szegő composition of polynomials, C. R. Acad. Sci. Paris Sér. I, Volume 343 (2006), pp. 81-86
[5] Polynomials, Algorithms and Computation in Mathematics, vol. 11, Springer-Verlag, Berlin, 2004
Cited by Sources: