Strong asymptotics for orthogoal polynomials with varying measures and Hermite-Padé approximants

13 pages, no figures.-- MSC1991 codes: 42C05; 30E10.-- Issue title: "Proceedings of the VIIIth Symposium on Orthogonal Polynomials and Their Application" (Seville, Spain, Sep. 1997), edited by Antonio J. Durán.MR#: MR1662686 (99i:42035)Zbl#: Zbl 0933.42017The strong asymptotic behaviour of orthogonal polynomials with respect to a general class of varying measures is given for the case of the unit circle and the real line. These results are used to obtain certain asymptotic relations for the polynomials involved in the construction of Hermite-Padé approximants of a Nikishin system of functions.The research of the second author (G.L.L.) was partially supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and by INTAS under grant 93-0219 EXT.Publicad