On the rank of Hermitian polynomials and the SOS Conjecture

Yun Gao, Sui-Chung Ng

Let $z\in {\mathbb{C}}^n$ and $\Vert z\Vert$ be its Euclidean norm. Ebenfelt proposed a conjecture regarding the possible ranks of the Hermitian polynomials in $z,\bar{z}$ of the form $A(z,\ba…