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).
@article{urn:eudml:doc:39966,
title = {A new rational and continuous solution for Hilbert's 17th problem.},
journal = {Extracta Mathematicae},
volume = {7},
year = {1992},
pages = {59-64},
mrnumber = {MR1203443},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39966}
}
Delzell, Charles N.; González-Vega, Laureano; Lombardi, Henri. A new rational and continuous solution for Hilbert's 17th problem.. Extracta Mathematicae, Tome 7 (1992) pp. 59-64. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39966/