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Ratio asymptotics of Hermite-Padé polynomials for Nikishin systems

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URI: http://hdl.handle.net/10016/6293
ISSN: 1064-5616
DOI: 10.1070/SM2005v196n08ABEH002329
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ratio_lagomasino_ms_2005_ps.pdf (276.78 KB)
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2005-08
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Turpion Ltd.
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Abstract
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 Nikishin system. For m=1 this result reduces to Rakhmanov's celebrated theorem on the ratio asymptotics for orthogonal polynomials on the real line.
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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 1077.42015
Keywords
Hermite-Padé orthogonal polynomials, Multiple orthogonal polynomials, Nikishin system, Varying measures, Ratio asymptotic
Bibliographic citation
Sbornik Mathematics c/c of Matematicheskii Sbornik, 2005, vol. 196, n. 8, p. 1089-1107
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