La composition de Schur–Szegö des polynômes et est définie comme . Dans le cas où P et Q sont hyperboliques, c. à d. n'ayant 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 .
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 .
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@article{CRMATH_2007__345_9_483_0, author = {Kostov, Vladimir Petrov}, title = {The {Schur{\textendash}Szeg\"o} composition for hyperbolic polynomials}, journal = {Comptes Rendus. Math\'ematique}, pages = {483--488}, publisher = {Elsevier}, volume = {345}, number = {9}, year = {2007}, doi = {10.1016/j.crma.2007.10.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.10.003/} }
TY - JOUR AU - Kostov, Vladimir Petrov TI - The Schur–Szegö composition for hyperbolic polynomials JO - Comptes Rendus. Mathématique PY - 2007 SP - 483 EP - 488 VL - 345 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.10.003/ DO - 10.1016/j.crma.2007.10.003 LA - en ID - CRMATH_2007__345_9_483_0 ER -
%0 Journal Article %A Kostov, Vladimir Petrov %T The Schur–Szegö composition for hyperbolic polynomials %J Comptes Rendus. Mathématique %D 2007 %P 483-488 %V 345 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.10.003/ %R 10.1016/j.crma.2007.10.003 %G en %F CRMATH_2007__345_9_483_0
Kostov, Vladimir Petrov. The Schur–Szegö composition for hyperbolic polynomials. Comptes Rendus. Mathématique, Tome 345 (2007) no. 9, pp. 483-488. doi : 10.1016/j.crma.2007.10.003. http://archive.numdam.org/articles/10.1016/j.crma.2007.10.003/
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[3] On arrangements of roots for a real hyperbolic polynomial and its derivatives, Bull. Sci. Math., Volume 126 (2002) no. 1, pp. 45-60
[4] Polynomials, Algorithms and Computation in Mathematics, vol. 11, Springer-Verlag, Berlin, 2004 (xiv+301 pp)
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⁎ Research partially supported by Wenner-Grenn Foundation.