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Sbornik: Mathematics, 2018, Volume 209, Issue 3, Pages 385–420
DOI: https://doi.org/10.1070/SM8724 (Mi sm8724) 		 
This article is cited in 8 scientific papers (total in 8 papers)

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

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

a Hidráulica y Ordenación del Territorio, Universidad Politécnica de Madrid, Madrid, Spain
b Department of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA
c Departamento de Matemáticas, Universidad Carlos III de Madrid, Madrid, Spain
English version PDF (693 kB) Citations (8) Russian version article
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DOI: https://doi.org/10.1070/SM8724
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-P
MTM2015-65888-C4-2
Simons Foundation
Received: 26.04.2016 and 20.01.2017
Bibliographic databases:
Document Type: Article
UDC: 517.538.3+517.538.5
MSC: Primary 30E10, 42C05; Secondary 41A20
Language: English
Original paper language: Russian
Citation: D. Barrios Rolanía, J. S. Geronimo, G. López Lagomasino, “High-order recurrence relations, Hermite-Padé approximation and Nikishin systems”, Sb. Math., 209:3 (2018), 385–420
Citation in format AMSBIB
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\by D.~Barrios Rolan{\'\i}a, J.~S.~Geronimo, G.~L\'opez Lagomasino
\paper High-order recurrence relations, Hermite-Pad\'e approximation and Nikishin systems
\jour Sb. Math.
\yr 2018
\vol 209
\issue 3
\pages 385--420
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  • https://doi.org/10.1070/SM8724
  • https://www.mathnet.ru/eng/sm/v209/i3/p102
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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