Asymptotics of orthogonal polynomials inside the unit circle and Szegő–Padé approximants

摘要

We study the asymptotic behavior of orthogonal polynomials inside the unit circle for a subclass of measures that satisfy Szegő's condition. We give a connection between such behavior and a Montessus de Ballore-type theorem for Szegő–Padé rational approximants of the corresponding Szegő function.