Abstract
We extend previous results about Putinar’s Positivstellensatz for cylinders of type S × ℝ to sets of type S × ℝr in some special cases, taking into account r and the degree of the polynomial with respect to the variables moving in ℝr (this is to say, in the non-bounded directions). These special cases are in correspondence with the ones where the equality between the cone of non-negative polynomials and the cone of sums of squares holds. Degree bounds are provided.
Acknowledgement
We are very grateful to Michel Coste for suggesting to us these extensions of our results from [9]
Funding: The authors were partially supported by the Argentinian grants UBACYT 20020190100116BA and PIP 11220130100527CO CONICET.
Communicated by: D. Plaumann
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