Constructive proofs of some positivstellens\"atze for compact   semialgebraic subsets of $\mathbb{R}^d$
  In a broad sense, positivstellens\"atze are results about representations of polynomials which are strictly positive on a given set. We give constructive and, to a large extent, elementary proofs of some known positivstellens\"atze for compact semialgebraic subsets of $\mathbb{R}^d$. The presented proofs extend and simplify arguments of Berr, W\"ormann (2001) and Schweighofer (2002, 2005). 
Gennadiy Averkov
math.AG math.AC math.OC