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 Mat. Sb., 2018, Volume 209, Number 3, Pages 102–137 (Mi msb8724)

High-order recurrence relations, Hermite-Padé approximation and Nikishin systems

D. Barrios Rolaníaa, J. S. Geronimob, G. López Lagomasinoc

b Department of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA

Abstract: The study of sequences of polynomials satisfying high-order recurrence relations is connected with the asymptotic behaviour of multiple orthogonal polynomials, the convergence properties of type II Hermite-Padé approximation and eigenvalue distribution of banded Toeplitz matrices. We present some results for the case of recurrences with constant coefficients which match what is known for the Chebyshev polynomials of the first kind. In particular, under appropriate assumptions, we show that the sequence of polynomials satisfies multiple orthogonality relations with respect to a Nikishin-type system of measures.
Bibliography: 20 titles.

Keywords: high-order recurrence relation, Hermite-Padé approximation, multiple orthogonality, Nikishin system.

 Funding Agency Grant Number Ministerio de Economía y Competitividad MTM2014-54053-PMTM2015-65888-C4-2 Simons Foundation

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8724

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English version:
Sbornik: Mathematics, 2018, 209:3, 385–420

Bibliographic databases:

UDC: 517.538.3+517.538.5
MSC: Primary 30E10, 42C05; Secondary 41A20

Citation: D. Barrios Rolanía, J. S. Geronimo, G. López Lagomasino, “High-order recurrence relations, Hermite-Padé approximation and Nikishin systems”, Mat. Sb., 209:3 (2018), 102–137; Sb. Math., 209:3 (2018), 385–420

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/msb8724
• https://doi.org/10.4213/sm8724
• http://mi.mathnet.ru/eng/msb/v209/i3/p102

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. S. P. Suetin, “On a new approach to the problem of distribution of zeros of Hermite–Padé polynomials for a Nikishin system”, Proc. Steklov Inst. Math., 301 (2018), 245–261
2. S. P. Suetin, “On an Example of the Nikishin System”, Math. Notes, 104:6 (2018), 905–914
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