Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets

Schweighofer, Markus

Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets

Dateien

semiring.pdfGröße: 1.58 MBDownloads: 270

Datum

2005

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

nonnegative polynomial, semiring, preprime, preorder, preordering, archimedean, Real Representation Theorem, Kadison-Dubois Theorem

Zitieren

ISO 690

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-z

BibTex

@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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