Nikishin systems are perfect. Case of unbounded and touching supports

Details Nikishin systems are perfect. Case of unbounded and touching supports Nikishin systems are perfect. Case of unbounded and touching supports

2010-09-10

arxiv.org/abs/1009.1922v1

Mathematics

Complex Variables

26 pages

Scientific paper

K. Mahler introduced the concept of perfect systems in the theory of simultaneous Hermite-Pad\'{e} approximation of analytic functions. Recently, we proved that Nikishin systems, generated by measures with bounded support and non-intersecting consecutive supports contained on the real line, are perfect. Here, we prove that they are also perfect when the supports of the generating measures are unbounded or touch at one point. As an application, we give a version of Stieltjes' theorem in the context of simultaneous Hermite-Pad\'e approximation.

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