General results on the convergence of multipoint Hermite-Padé approximants of Nikishin systems

19 pages, no figures.-- MSC1991 codes: Primary 30E10, 42C05.MR#: MR2263738 (2007g:42041)Zbl#: Zbl 1105.30024We consider simultaneous approximation of Nikishin systems of functions by means of rational vector functions which are constructed interpolating along a prescribed table of points. We give general conditions for the uniform convergence of such approximants with a geometric rate under very weak assumptions.The work of both authors was supported by Ministerio de Ciencia y Tecnología under grant BFM 2003-06335-C03-02. The second author was also partially supported by NATO PST.CLG.979738 and INTAS 03-51-6637.Publicad