A new rational and continuous solution for the Hilbert's 17 th problem
-
Autores: Laureano González Vega
, C. N. Dellzell, Henri Lombardi
- Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 7, Nº 1, 1992, págs. 59-64
- Idioma: inglés
- Enlaces
-
Resumen
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
¿Es nuevo? Regístrese
Ventajas de registrarse
