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Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets

Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets

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SCHWEIGHOFER, Markus, 2005. Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets. In: manuscripta mathematica. 117(4), pp. 407-428. ISSN 0025-2611

@article{Schweighofer2005Certi-15645, title={Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets}, year={2005}, doi={10.1007/s00229-005-0568-z}, number={4}, volume={117}, issn={0025-2611}, journal={manuscripta mathematica}, pages={407--428}, author={Schweighofer, Markus} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/15645"> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-11-09T11:13:31Z</dc:date> <dcterms:title>Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets</dcterms:title> <dcterms:bibliographicCitation>First publ. in: Manuscripta Mathematica 117 (2005), 4. - S. 407-428</dcterms:bibliographicCitation> <dc:language>eng</dc:language> <dcterms:issued>2005</dcterms:issued> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-11-09T11:13:31Z</dcterms:available> <dc:creator>Schweighofer, Markus</dc:creator> <dc:contributor>Schweighofer, Markus</dc:contributor> <dcterms:rights rdf:resource="http://nbn-resolving.org/urn:nbn:de:bsz:352-20140905103605204-4002607-1"/> <dcterms:abstract xml:lang="eng">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.</dcterms:abstract> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/15645"/> <dc:rights>deposit-license</dc:rights> </rdf:Description> </rdf:RDF>

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