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También publicado en arXiv:1307.0213 Abstract: Fade approximation has two natural extensions to vector rational approximation through the so-called type I and type II Hermite-Pade approximants. The convergence properties of type II Hermite-Pade approximants have been studied. For such approximants Markov and Stieltjes type theorems are available. To the present, such results have not been obtained for type I approximants. In this paper, we provide Markov and Stieltjes type theorems on the convergence of type I Hermite-Pade approximants for Nikishin systems of functions.
multiple orthogonal polynomials; nikishin systems; type i hermite-padé approximants