Bernstein-Szego measures on the two dimensional torus

We present a new viewpoint (namely, reproducing kernels) and new proofs for several recent results of J. Geronimo and H. Woerdeman on orthogonal polynomials on the two dimensional torus (and re-lated subjects). In addition, we show how their results give a new proof of Andô's inequality via an equivalent version proven by Cole and Wermer. A major theme is the use of so-called Bernstein-Szego measures. A simple necessary and sufficient condition for two variable polynomial stability is also given.