Root arrangements of hyperbolic polynomial-like functions.

Título inglés	Root arrangements of hyperbolic polynomial-like functions.
Título español	Ordenaciones de raíces de funciones asimiladas a polinomios hiperbólicos.
Autor/es	Kostov, Vladimir Petrov
Organización	Lab. Math. Univ. Nice, Niza, Francia
Revista	1139-1138
Publicación	2006, 19 (1): 197-225, 9 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	A real polynomial P of degree n in one real variable is hyperbolic if its roots are all real. A real-valued function P is called a hyperbolic polynomial-like function (HPLF) of degree n if it has n real zeros and P(n) vanishes nowhere. Denote by xk(i) the roots of P(i), k = 1, ..., n-i, i = 0, ..., n-1. Then in the absence of any equality of the form xi(j) = xk(i)               (1) one has "i < j      xk(i) < xk(j) < xk+j-i(i)               (2) (the Rolle theorem). For n ≥ 4 (resp. for n ≥ 5) not all arrangements without equalities (1) of n(n+1)/2 real numbers xk(i) and compatible with (2) are realizable by the roots of hyperbolic polynomials (resp. of HPLFs) of degree n and of their derivatives. For n = 5 and when x1(1) < x2(1) < x1(3) < x2(3) < x3(1) < x4(1) we show that from the 40 arrangements without equalities (1) and compatible with (2) only 16 are realizable by HPLFs (from which 6 by perturbations of hyperbolic polynomials and none by hyperbolic polynomials).
Clasificación UNESCO	120113 ; 120210
Palabras clave español	Ceros de polinomios ; Ceros de una función
Código MathReviews	MR2219829
Código Z-Math	Zbl pre05042417
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