Summary: Polynomial optimization on odd-dimensional spheres
John P. D'Angelo and Mihai Putinar
Abstract. The sphere S2d-1
naturally embeds into the complex affine space
. We show how the complex variables in Cd
simplify the known Striktpos-
itivstellens¨atze, when the supports are resticted to semi-algebraic subsets of
odd dimensional spheres.
Mathematics Subject Classification (2000). Primary 14P10; Secondary 32A70.
Keywords. Positive polynomial, Hermitian square, unit sphere, plurisubhar-
denote complex Euclidean space with Euclidean norm given by |z|2
. The unit, odd dimensional sphere