2014/11/17 by Christoph Schulze, Schulze, Christoph
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical and Theoretical Analysis #Mathematics and Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1411.4446
openalex publication_date 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a translation of a final paper. It contains proofs of some well-known Positivstellensätze. The approach in this paper differs in two respects from presentations in literature. We use the Stone-Weierstrass Theorem directly to prove an inductive property, which makes the Kadison-Dubois Theorem superfluous in our paper, and we also consider homogeneous and projective Positivstellensätze. This leads us to a homogeneous version of Schmüdgen's theorem and a projective version of Putinar's theorem.