Journal of Applied Mathematics 
Volume 2004 (2004), Issue 1, Pages 37-53
doi:10.1155/S1110757X04304092

Asymptotics for orthogonal polynomials off the circle

R. Khaldi and R. Benzine

Department of Mathematics, University of Annaba, BP 12, Annaba 2300, Algeria

Received 29 April 2003; Revised 30 September 2003

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.