Asymptotics for orthogonal polynomials off the circle

Abstract

We study the strong asymptotics of orthogonal polynomials with respect to a measure of the type dμ/2π+∑j=1∞Ajδ(z−zk), where μ is a positive measure on the unit circle Γ satisfying the Szegö condition and {zj}j=1∞ are fixed points outside Γ. The masses {Aj}j=1∞ are positive numbers such that ∑j=1∞Aj<+∞. Our main result is the explicit strong asymptotic formulas for the corresponding orthogonal polynomials.