Asymptotics for orthogonal polynomials off the circle

Abstract

We study the strong asymptotics of orthogonal polynomials with respect to a measure of the type $d\mu /2\pi +{\sum }_{j=1}^{\infty }{A}_j\delta \left(z-z_k\right)$, where $\mu$ is a positive measure on the unit circle $\Gamma$ satisfying the Szegö condition and ${\left\{z_j\right\}}_{j=1}^{\infty }$ are fixed points outside $\Gamma$. The masses ${\left\{A_j\right\}}_{j=1}^{\infty }$ are positive numbers such that . Our main result is the explicit strong asymptotic formulas for the corresponding orthogonal polynomials.