Ratio asymptotics of Hermite-Padé polynomials for Nikishin systems

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©, 2005 Russian Academy of Sciences, (DoM) and London Mathematical Society, Turpion Ltd
, , Citation A I Aptekarev et al 2005 Sb. Math. 196 1089 DOI 10.1070/SM2005v196n08ABEH002329

1064-5616/196/8/1089

Abstract

The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of  finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.

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10.1070/SM2005v196n08ABEH002329