Fejér-Riesz factorizations and the structure of bivariate polynomials orthogonal on the bi-circle

Jeffrey S. Geronimo, Plamen Iliev

We give a complete characterization of the positive trigonometric polynomials Q(θ,ϕ) on the bi-circle, which can be factored as Q(θ,ϕ)=|p(e^{iθ},e^{iϕ})|^2 where p(z,w) is a polyno…