Positive Polynomials with Zeros

Chapter 6 studies extensions of the strict positivstellensätze from Chapter 5 to non-negative polynomials. The most important tool is the Archimedean local-global principle, which is given an independent second proof. Combining this result with an analysis of (weighted) sums of squares in local rings, a series of existence and non-existence results is obtained for sums of squares representations of non-negative polynomials.