A criterion for positive polynomials

Details A criterion for positive polynomials A criterion for positive polynomials

2003-12-26

arxiv.org/abs/math/0312469v2

Mathematics

Algebraic Geometry

Several minor changes and new Prop. (1.15)

Scientific paper

Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity and a sufficient condition for non-negativity, in terms of positivity or semi-positivity of a one-variable characteristic polynomial of F. Also, we review another well-known sufficient condition.

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