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 |
Acceso al artículo completo |