Title: Bernstein-Szeg\"o measures on the two dimensional torus

Authors: Greg Knese

Issue: Volume 57 (2008), Issue 3, 1353-1376

Abstract: 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 related subjects). In addition, we show how their results give a new proof of And\^{o}'s inequality via an equivalent version proven by Cole and Wermer. A major theme is the use of so-called Bernstein-Szeg\"{o} measures. A simple necessary and sufficient condition for two variable polynomial stability is also given.