Quadratic modules of polynomials in two variables

Prestel, Alexander; Cabral, Eugenia

Quadratic modules of polynomials in two variables

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Date

2008

Authors

Prestel, Alexander

Cabral, Eugenia

Publication type

Journal article

Published in

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].

Subject (DDC)

510 Mathematics

Cite This

ISO 690

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.2008.014

BibTex

@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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