Geodesic
Hermite--Pad\'e approximation for Nikishin systems of analytic functions
Sbornik. Mathematics, Tome 77 (1994) no. 2, pp. 367-384

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Nikishin type systems of analytic functions are considered. For such systems, convergence of the main diagonal of the associated Hermite-Padé approximants is proved, when interpolation is equally distributed between the functions. If interpolation is 'nearly' equally distributed, then convergence in capacity takes place. Multipoint Padé approximation plays a key role in the proof. 
@article{SM_1994_77_2_a7,
     author = {Zh. Bustamante and G. L\'opez Lagomasino},
     title = {Hermite--Pad\'e approximation for {Nikishin} systems of analytic functions},
     journal = {Sbornik. Mathematics},
     pages = {367--384},
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     volume = {77},
     number = {2},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_77_2_a7/}
}
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Zh. Bustamante; G. López Lagomasino. Hermite--Pad\'e approximation for Nikishin systems of analytic functions. Sbornik. Mathematics, Tome 77 (1994) no. 2, pp. 367-384. http://geodesic.mathdoc.fr/item/SM_1994_77_2_a7/