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

Charles N. Delzell, Laureano González-Vega, Henri Lombardi (1992)

Extracta Mathematicae

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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...