A criterion for positive polynomials

Fernando Cukierman

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A criterion for positive polynomials

Fernando Cukierman

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Abstract

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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Fernando Cukierman. 2004-07-28. A criterion for positive polynomials. https://arxiv.org/abs/math/0312469

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