A version of Putinar's Positivstellensatz for cylinders.

PAULA ESCORCIELO; DANIEL PERRUCCI

JOURNAL OF PURE AND APPLIED ALGEBRA

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2020 vol. 224

0022-4049

We prove that, under some additional assumption, Putinar?s Positivstellensatz holds on cylinders of type S×R with S={x∈Rn | g1(x)≥0,...,gs(x)≥0} such that the quadratic module generated by g1,...,gs in R[X1,...,Xn] is archimedean, and we provide a degree bound for the representation of a polynomial f ∈ R[X1,...,Xn,Y] which is positive on S×R as an explicit element of the quadratic module generated by g1,...,gs in R[X1,...,Xn,Y]. We also include an example to show that an additional assumption is necessary for Putinar?s Positivstellensatz to holdon cylinders of this type.