Quadratic modules of polynomials in two variables
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 ; 8 (2008), 2. - pp. 189-204
Abstract
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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PRESTEL, Alexander, Eugenia CABRAL, 2008. Quadratic modules of polynomials in two variables. In: Advances in Geometry. 8(2), pp. 189-204. Available under: doi: 10.1515/ADVGEOM.2008.014BibTex
@article{Prestel2008Quadr-790, 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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