A criterion for positive polynomials
代数几何
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0312469,
title = {A criterion for positive polynomials},
author = {Fernando Cukierman},
journal= {arXiv preprint arXiv:math/0312469},
year = {2007}
}
备注
Several minor changes and new Prop. (1.15)