Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets
| dc.contributor.author | Schweighofer, Markus | |
| dc.date.accessioned | 2011-11-09T11:13:31Z | deu |
| dc.date.available | 2011-11-09T11:13:31Z | deu |
| dc.date.issued | 2005 | |
| dc.description.abstract | 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. | eng |
| dc.description.version | published | |
| dc.identifier.citation | First publ. in: Manuscripta Mathematica 117 (2005), 4. - S. 407-428 | deu |
| dc.identifier.doi | 10.1007/s00229-005-0568-z | deu |
| dc.identifier.ppn | 352876786 | deu |
| dc.identifier.uri | http://kops.uni-konstanz.de/handle/123456789/15645 | |
| dc.language.iso | eng | deu |
| dc.legacy.dateIssued | 2011-11-09 | deu |
| dc.rights | terms-of-use | deu |
| dc.rights.uri | https://rightsstatements.org/page/InC/1.0/ | deu |
| dc.subject | nonnegative polynomial | deu |
| dc.subject | semiring | deu |
| dc.subject | preprime | deu |
| dc.subject | preorder | deu |
| dc.subject | preordering | deu |
| dc.subject | archimedean | deu |
| dc.subject | Real Representation Theorem | deu |
| dc.subject | Kadison-Dubois Theorem | deu |
| dc.subject.ddc | 510 | deu |
| dc.title | Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets | eng |
| dc.type | JOURNAL_ARTICLE | deu |
| dspace.entity.type | Publication | |
| kops.citation.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}
} | |
| kops.citation.iso690 | 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 | deu |
| kops.citation.iso690 | 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 | eng |
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| kops.identifier.nbn | urn:nbn:de:bsz:352-156459 | deu |
| kops.sourcefield | manuscripta mathematica. 2005, <b>117</b>(4), pp. 407-428. ISSN 0025-2611. Available under: doi: 10.1007/s00229-005-0568-z | deu |
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