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Hermite–Padé approximation for Nikishin systems of analytic functions

Zh. Bustamante, G. López Lagomasino


Abstract: 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.

UDC: 517.53

MSC: Primary 30E10; Secondary 41A21

Received: 15.10.1991

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:2, 367–384

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