Strong asymptotics for Sobolev orthogonal polynomials in the complex plane

We obtain the strong asymptotics for the sequence of monic polynomials minimizing the norm‖q‖S=(∑k=0N‖q(k)‖k2)1/2, where ‖⋅‖k, k=0,…,N−1, are L2 norms with respect to measures supported on the same rectifiable Jordan closed curve or arc Γ, and ‖⋅‖N is the L2 norm corresponding to a weight supported on Γ, which satisfies the Szegő condition, plus mass points in the unbounded connected component of C∖Γ.