Positive polynomials on nondegenerate basic semi-algebraic sets
Huy-Vui Hà, Ho Minh Toan · Advances in Geometry · 2016
Abstract A concept of nondegenerate basic closed semi-algebraic sets in ℝnis introduced. These areunboundedclosed semi-algebraic sets for which we obtain some representations of polynomials with positive infima (the polynomials are further assumed to be bounded ifn>2) and solutions of the moment problem. The key to obtain these results is an explicit description of the algebra of bounded polynomials on a nondegenerate basic semi-algebraic set via the combinatorial information of the Newton polyhedron corresponding to the generators of the semi-algebraic set.