Ratio asymptotics of Hermite-Padé polynomials for Nikishin systems

19 pages, no figures.-- MSC2000 codes: Primary 42C05, 41A21.-- Originally published in Russian language by the Russian Academy of Mathematics in: Matematicheskii Sbornik 196(8): 3–20 (2005).Zbl#: Zbl 1077.42015The existence of ratio asymptotics is proved for a sequence of multiple orthogonal polynomials with orthogonality relations distributed among a system of m finite Borel measures with support on a bounded interval of the real line which form a so-called Nikishin system. For m=1 this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.The research of the first author was carried out with the support of the Russian Foundation for Basic Research (grant no. 02-01-00564), the Programme of Support of Leading Scientific Schools of RF (grant no. NSh-1551.2003.1), the RAS Programme ‘Current Problems of Theoretical Mathematics’, INTAS (grant no. 03-516637) and NATO PST.CLG (grant no. 979738). The research of the second author was carried out with the support of INTAS (grant no. 03-516637), NATO PST.CLG (grant no. 979738), and BFM (grant no. 2003-06335-C03-02). The research of the third author was carried out with the support BFM (grant no. 2003-06335-C03-02).Publicad