Cita:
Sbornik Mathematics c/c of Matematicheskii Sbornik, 2005, vol. 196, n. 8, p. 1089-1107
ISSN:
1064-5616
DOI:
10.1070/SM2005v196n08ABEH002329
Agradecimientos:
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).
The 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 NikishiThe 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.[+][-]
Nota:
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).
