Publikation: Quadratic modules of polynomials in two variables
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2008
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Cabral, Eugenia
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Advances in Geometry. 2008, 8(2), pp. 189-204. Available under: doi: 10.1515/ADVGEOM.2008.014
Zusammenfassung
Let h1, , R[X, Y] and assume that the set W (h) := {(a, b) 2 | hi(a, b) ≥ 0 for all 1 ≤ i ≤ s} is compact and non-empty. We give an effective method to decide from the knowledge of h1, , hs whether every polynomial R[X, Y], strictly positive on W(h), has a representation f = σ0 + h1σ1 +···+ hsσs with each σi being a sum of squares in R[X, Y].
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510 Mathematik
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PRESTEL, Alexander, Eugenia CABRAL, 2008. Quadratic modules of polynomials in two variables. In: Advances in Geometry. 2008, 8(2), pp. 189-204. Available under: doi: 10.1515/ADVGEOM.2008.014BibTex
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year={2008},
doi={10.1515/ADVGEOM.2008.014},
title={Quadratic modules of polynomials in two variables},
number={2},
volume={8},
journal={Advances in Geometry},
pages={189--204},
author={Prestel, Alexander and Cabral, Eugenia}
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<dcterms:abstract xml:lang="eng">Let h1, , R[X, Y] and assume that the set W (h) := {(a, b) 2 | hi(a, b) ≥ 0 for all 1 ≤ i ≤ s} is compact and non-empty. We give an effective method to decide from the knowledge of h1, , hs whether every polynomial R[X, Y], strictly positive on W(h), has a representation f = σ0 + h1σ1 +···+ hsσs with each σi being a sum of squares in R[X, Y].</dcterms:abstract>
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