Strong asymptotics for Sobolev orthogonal polynomials

14 pages, no figures.-- MSC1991 codes: 42C05, 33C25.Zbl 0937.42011In this paper we obtain the strong asymptotics for the sequence of orthogonal polynomials with respect to the inner product$$ \langle f,g,\rangle=\sum_{k=0}\sp n \int_{\Delta_k} f\sp (k)}(x)g\sp (k)}(x) d\mu_k(x), $$where $\{\mu_k\}_k=0\sp m, $ with m ∈ Z+ are measures supported on [−1,1] which satisfy Szegö's condition.Research by first author (A.M.F.) was partially supported by a research grant from Dirección General de Enseñanza Superior (DGES) of Spain, project code PB95-1205, a research grant from the European Economic Community, INTAS-93-219-ext, and by Junta de Andalucía, Grupo de Investigación FQM 0229.Publicad