Real Algebraic and Analytic Geometry

Preprint Server

Previous   Next
135. Markus Schweighofer:
Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets.


Submission: 2005, April 17.

We prove a criterion for an element of a commutative ring to be contained in an archimedean subsemiring. It can be used to investigate the question whether nonnegativity of a polynomial on a compact semialgebraic set can be certified in a certain way. In case of (strict) positivity instead of nonnegativity, our criterion simplifies to classical results of Stone, Kadison, Krivine, Handelman, Schmüdgen et al. As an application of our result, we give a new proof of the following result of Handelman: If an odd power of a real polynomial in several variables has only nonnegative coefficients, then so do all sufficiently high powers.

Mathematics Subject Classification (2000): 13J25, 13J30, 16Y60, 26C99, 54H10.

Keywords and Phrases: nonnegative polynomial, semiring, preprime, preorder, preordering, archimedean, Real Representation Theorem, Kadison-Dubois Theorem.

Full text, 21p.: dvi 113k, ps.gz 219k, pdf 278k.

Server Home Page