Constructive proofs of some positivstellensätze for compact semialgebraic subsets of $\mathbb{R}^d$

Details Constructive proofs of some positivstellensätze for compact semialgebraic subsets of $\mathbb{R}^d$ Constructive proofs of some positivstellensätze for compact semialgebraic subsets of $\mathbb{R}^d$

2012-01-19

arxiv.org/abs/1201.4066v2

Mathematics

Algebraic Geometry

Scientific paper

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).

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