Smooth parametrizations for several cases of the Positivstellensatz

pdf file.
with González-Vega L.
Math. Zeitschrift 225, (1997), 427-451.

Abstract : We give smooth parametrizations (Cr, C or Nash) for several cases of the Positivstellensatz. This improves previous results where the parametrizations were obtained by means of semipolynomials (sup-inf combination of polynomial functions). A general homogeneous Positivstellensatz is obtained and used to get several homogeneous versions of the parametrization theorems.