Publikation: Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets
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2005
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manuscripta mathematica. 2005, 117(4), pp. 407-428. ISSN 0025-2611. Available under: doi: 10.1007/s00229-005-0568-z
Zusammenfassung
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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
nonnegative polynomial, semiring, preprime, preorder, preordering, archimedean, Real Representation Theorem, Kadison-Dubois Theorem
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SCHWEIGHOFER, Markus, 2005. Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets. In: manuscripta mathematica. 2005, 117(4), pp. 407-428. ISSN 0025-2611. Available under: doi: 10.1007/s00229-005-0568-zBibTex
@article{Schweighofer2005Certi-15645,
year={2005},
doi={10.1007/s00229-005-0568-z},
title={Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets},
number={4},
volume={117},
issn={0025-2611},
journal={manuscripta mathematica},
pages={407--428},
author={Schweighofer, Markus}
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