Un polynôme réel d'une variable est hyperbolique si toutes ses racines sont réelles. Un polynôme hyperbolique est très hyperbolique s'il a des primitives hyperboliques de tout ordre. Un polynôme P est stablement hyperbolique si est hyperbolique pour certains et Q (polynôme de degré ). Nous présentons des propriétés géométriques des domaines de polynômes très hyperboliques et stablement hyperboliques dans la famille .
A real polynomial in one variable is hyperbolic if it has only real roots. A hyperbolic polynomial is very hyperbolic if it has hyperbolic primitives of all orders. A polynomial P is stably hyperbolic if is hyperbolic for suitable and Q (polynomial of degree ). We present some geometric properties of the domains of very hyperbolic and of stably hyperbolic polynomials in the family .
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@article{CRMATH_2004__339_3_157_0, author = {Kostov, Vladimir Petrov}, title = {Very hyperbolic and stably hyperbolic polynomials}, journal = {Comptes Rendus. Math\'ematique}, pages = {157--162}, publisher = {Elsevier}, volume = {339}, number = {3}, year = {2004}, doi = {10.1016/j.crma.2004.05.010}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2004.05.010/} }
TY - JOUR AU - Kostov, Vladimir Petrov TI - Very hyperbolic and stably hyperbolic polynomials JO - Comptes Rendus. Mathématique PY - 2004 SP - 157 EP - 162 VL - 339 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2004.05.010/ DO - 10.1016/j.crma.2004.05.010 LA - en ID - CRMATH_2004__339_3_157_0 ER -
%0 Journal Article %A Kostov, Vladimir Petrov %T Very hyperbolic and stably hyperbolic polynomials %J Comptes Rendus. Mathématique %D 2004 %P 157-162 %V 339 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2004.05.010/ %R 10.1016/j.crma.2004.05.010 %G en %F CRMATH_2004__339_3_157_0
Kostov, Vladimir Petrov. Very hyperbolic and stably hyperbolic polynomials. Comptes Rendus. Mathématique, Tome 339 (2004) no. 3, pp. 157-162. doi : 10.1016/j.crma.2004.05.010. http://archive.numdam.org/articles/10.1016/j.crma.2004.05.010/
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