Strong asymptotics for Sobolev orthogonal polynomials in the complex plane

15 pages, no figures.-- MSC2000 codes: 42C05, 33C25.MR#: MR2376173Zbl#: Zbl 1154.33303^aWe obtain the strong asymptotics for the sequence of monic polynomials minimizing the norm $$\Vert q_S\Vert=(\sum_{k=0}^N \Vert q^{(k)}\Vert_k^2)^{1/2}$$ where $\Vert \bullet\Vert_k$, $k=0,\dots, N-1$, are $L^2$ norms with respect to measures supported on the same rectifiable Jordan closed curve on $\Gamma$, and $\Vert \bullet\Vert_N$ is the $L^2$ norm corresponding to a weight supported or arc $\Gamma$, which satisfies the Szegö condition, plus mass points in the unbounded connected component of $\bbfC\setminus \Gamma$.First author's research partially supported by Ministerio de Ciencia y Tecnología, grant MTM2006-13000-C03-02 and by Comunidad de Madrid-Universidad Carlos III de Madrid, grant CCG06-UC3M/EST-0690. Second author's research partially supported by Ministerio de Ciencia y Tenología, project code MTM2005-09648-C02-01 and by Junta de Andalucía, FQM-229, FQM-481 and P06-FQM-01738. Fourth author's research partially supported by a research grant from Centro de Investigación Matemática de Canarias (CIMAC), Spain.Publicad