A new rational and continuous solution for Hilbert's 17th problem.

Título inglés	A new rational and continuous solution for Hilbert's 17th problem.
Título español	Una nueva solución racional y continua para el decimoséptimo problema de Hilbert.
Autor/es	Delzell, Charles N. ; González-Vega, Laureano ; Lombardi, Henri
Organización	Dep. Math. Louisiana State Univ., Louisiana, Estados Unidos;Dep. Mat. Estad. Comp. Univ. Cantabria, Santander, España;Lab. Math. Univ. Franche-Comté, Besançon, Francia
Revista	0213-8743
Publicación	1992, 7 (1): 59-64, 7 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	In this note it is presented a new rational and continuous solution for Hilbert's 17th problem, which asks if an everywhere positive polynomial can be expressed as a sum of squares of rational functions. This solution (Theorem 1) improves the results in [2] in the sense that our parametrized solution is continuous and depends in a rational way on the coefficients of the problem (what is not the case in the solution presented in [2]). Moreover our method simplifies the proof and it is easy to generalize to other situations: for example in [4 or 5] we improve the results obtained in [7] giving more general rational and continuous solutions for several instances of Positivstellensatz (Theorem 2).
Clasificación UNESCO	120101
Palabras clave español	Problema 17 de Hilbert ; Campos ordenados ; Análisis constructivo
Código MathReviews	MR1203443
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