Sums of squares on real algebraic curves


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SCHEIDERER, Claus, 2003. Sums of squares on real algebraic curves. In: Mathematische Zeitschrift. 245(4), pp. 725-760. ISSN 0025-5874. eISSN 1432-1823

@article{Scheiderer2003squar-23302, title={Sums of squares on real algebraic curves}, year={2003}, doi={10.1007/s00209-003-0568-1}, number={4}, volume={245}, issn={0025-5874}, journal={Mathematische Zeitschrift}, pages={725--760}, author={Scheiderer, Claus} }

<rdf:RDF xmlns:rdf="" xmlns:bibo="" xmlns:dc="" xmlns:dcterms="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dcterms:abstract xml:lang="eng">Given an affine algebraic variety V over ℝ with real points V(ℝ) compact and a non-negative polynomial function f∈ℝ[V] with finitely many real zeros, we establish a local-global criterion for f to be a sum of squares in ℝ[V]. We then specialize to the case where V is a curve. The notion of virtual compactness is introduced, and it is shown that in the local-global principle, compactness of V(ℝ) can be relaxed to virtual compactness. The irreducible curves on which every non-negative polynomial is a sum of squares are classified. All results are extended to the more general framework of preorders. Moreover, applications to the K-moment problem from analysis are given. In particular, Schmüdgen’s solution of the K-moment problem for compact K is extended, for dim (K)=1, to the case when K is virtually compact.</dcterms:abstract> <dcterms:available rdf:datatype="">2013-05-17T08:57:29Z</dcterms:available> <dc:contributor>Scheiderer, Claus</dc:contributor> <dc:rights>deposit-license</dc:rights> <dc:date rdf:datatype="">2013-05-17T08:57:29Z</dc:date> <dc:creator>Scheiderer, Claus</dc:creator> <bibo:uri rdf:resource=""/> <dcterms:issued>2003</dcterms:issued> <dc:language>eng</dc:language> <dcterms:title>Sums of squares on real algebraic curves</dcterms:title> <dcterms:bibliographicCitation>Mathematische Zeitschrift ; 245 (2003), 4. - S. 725-760</dcterms:bibliographicCitation> <dcterms:rights rdf:resource=""/> </rdf:Description> </rdf:RDF>

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