Weak convergence of varying measures and Hermite-Padé orthogonal polynomials

23 pages, no figures.-- MSC1991 codes: 42C05, 30E10.MR#: MR1702795 (2000j:42036)Zbl#: Zbl 1058.42503It is known that the common denominator of the Hermite-Padé approximants of a mixed Angelesco-Nikishin system shares orthogonality relations with respect to each function in the system. It is less well known that they also satisfy full orthogonality with respect to a varying measure. This problem motivates our interest in extending the class of varying measures with respect to which weak asymptotics of orthogonal polynomials takes place. In particular, for the case of a Nikishin system, we prove weak asymptotics of the corresponding varying measures.Research by second author (G.L.L.) was supported by Dirección General de Enseñanza Superior under grant PB 96-0120-C03-01 and by INTAS under grant 93-0219 EXT.Publicad