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
  • Texto completo (pdf)
• 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