Rate of convergence of generalized Hermite-Padé approximants of Nikishin systems

32 pages, no figures.-- MSC1991 code: Primary, 42CD5.MR#: MR2186304 (2006h:41017)Zbl#: Zbl 1136.42306We study the rate of convergence of interpolating simultaneous rational approximations with partially prescribed poles to so-called Nikishin systems of functions. To this end, a vector equilibrium problem in the presence of a vector external field is solved which is used to describe the asymptotic behavior of the corresponding second-type functions which appear.The work of both authors was supported by the 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