Sur le 17ème problème de Hilbert pour les fonctions de Nash

Abstract

The purpose of this note is to give a more refined version of a theorem of Efroymson: If U ⊂ R n U \subset {{\mathbf {R}}^n} is defined by polynomial inequalities of the form f i > 0 , i = 1 , … , p {f_i} > 0,i = 1, \ldots ,p , and if g is a positive definite Nash function on U, then g is a finite sum of squares of Nash meromorphe functions on U.