Parameters Associated with Bivariate Bernstein–Szegő Measures on the Bi-circle

摘要

We consider measures supported on the bi-circle and review the recurrence relations satisfied by the orthogonal polynomials associated with these measures constructed using the lexicographical or reverse lexicographical ordering. New relations are derived among these recurrence coefficients. We extend the results of (SIAM J Matrix Anal. Appl. 29, 796–825, 2007) on a parameterization for Bernstein–Szegő measures supported on the bi-circle.