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Journal of Applied Mathematics
Volume 2004 (2004), Issue 1, Pages 37-53
http://dx.doi.org/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 Hindawi Publishing Corporation. 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=1Ajδ(zzk), 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=1Aj<+. Our main result is the explicit strong asymptotic formulas for the corresponding orthogonal polynomials.