Putinar's Positivstellensatz is one of the most important
results in the theory of sums of squares and certificates of non-negativity.
This theorem states that given g1, ..., gs in R[X1, ..., Xn] such that
the quadratic module
M(g1, ..., gs) generated by g1, ..., gs is archimedean, every
f in R[X1, ..., Xn] positive on
S = {x in R^n | g1(x) >= 0, ..., gs(x) >= 0}
belongs to M(g1, ..., gs), which is a certificate of the non-negativity of f.
The condition of M(g1, ..., gs) being archimedean implies that the set
S is compact.
In this talk, we will present a version of Putinar's Positivstellensatz,
which under some aditional assumptions holds on cylinders
of type SxR. We will also present degree bounds.
This talk is based in a joint work with Paula Escorcielo.
