Asymptotic behavior of orthogonal rational functions corresponding to measure with discrete part off the unit circle (Q1360213)

Consider two measures, \(\mu_1\) entirely supported on the unit circle, and \(\mu_2\) equal to \(\mu_1\) plus a finite number of mass points which lie off the unit circle. Consider the respective sequences of orthogonal rational functions \(\{\phi_n\}\) and \(\{\varphi_n\}\), with poles fixed along a Newtonian table of points. The author gives sufficient conditions on the measure \(\mu\) and the table of fixed poles in order that \(\frac{\varphi_n}{\phi_n}\) converge uniformly on compact subsets of the exterior of the unit circle as \(n\) tends to \(\infty\).