Journal of Applied Mathematics
Volume 2004 (2004), Issue 1, Pages 37-53
doi:10.1155/S1110757X04304092
Asymptotics for orthogonal polynomials off the circle
Department of Mathematics, University of Annaba, BP 12, Annaba 2300, Algeria
Received 29 April 2003; Revised 30 September 2003
Copyright © 2004 R. Khaldi and R. Benzine. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.