Strong asymptotics for Sobolev orthogonal polynomials in the complex plane

摘要

We obtain the strong asymptotics for the sequence of monic polynomials minimizing the norm parallel to q parallel to(S) = (Sigma(N)(k=0)parallel to q((k))parallel to(2)(k))(1/2), where parallel to (.) parallel to(k), k = 0,..., N - 1, are L-2 norms with respect to measures supported on the same rectifiable Jordan closed curve or arc Gamma, and parallel to (.) parallel to(N) is the L2 norm corresponding to a weight supported on Gamma, which satisfies the Szego condition, plus mass points in the unbounded connected component of C Gamma. (c) 2007 Published by Elsevier Inc.