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Mat. Sb., 2018, Volume 209, Number 7, Pages 106–138 (Mi msb8889)  

This article is cited in 3 scientific papers (total in 3 papers)

Riemann-Hilbert analysis for a Nikishin system

G. López Lagomasinoa, W. Van Asscheb

a Departamento de Matemáticas, Universidad Carlos III de Madrid, Madrid, Spain
b Department of Mathematics, Katholieke Universiteit Leuven, Leuven, Belgium

Abstract: In this paper we give the asymptotic behaviour of type I multiple orthogonal polynomials for a Nikishin system of order two with two disjoint intervals. We use the Riemann-Hilbert problem for multiple orthogonal polynomials and steepest descent analysis for oscillatory Riemann-Hilbert problems to obtain the asymptotic behaviour in all the relevant regions of the complex plane.
Bibliography: 38 titles.

Keywords: multiple orthogonal polynomials, Riemann-Hilbert problem, Hermite-Padé approximations, asymptotic.

Funding Agency Grant Number
Ministerio de Economía y Competitividad MTM 2015-65888-C4-2-P
KU Leuven OT/12/073
Fonds Wetenschappelijk Onderzoek G.0864.13
G.0864.16N
G. López Lagomasino's research was supported by the Ministerio de Economía y Competitividad, Spain (grant MTM2015-65888-C4-2-P). W. Van Assche's research was supported by the Katholieke Universiteit Leuven (grant OT/12/073) and the Fonds Wetenschappelijk Onderzoek (projects G.0934.13, G.0864.16N).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8889

Full text: PDF file (1102 kB)
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English version:
Sbornik: Mathematics, 2018, 209:7, 1019–1050

Bibliographic databases:

UDC: 517.538.3+517.538.7
MSC: 30E10, 30E25, 41A21, 42C05
Received: 21.12.2016 and 06.12.2017

Citation: G. López Lagomasino, W. Van Assche, “Riemann-Hilbert analysis for a Nikishin system”, Mat. Sb., 209:7 (2018), 106–138; Sb. Math., 209:7 (2018), 1019–1050

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  mathnet  crossref  crossref  isi  elib  elib
    2. S. P. Suetin, “On an Example of the Nikishin System”, Math. Notes, 104:6 (2018), 905–914  mathnet  crossref  crossref  isi  elib
    3. S. P. Suetin, “O suschestvovanii trekhlistnoi poverkhnosti Nattolla v nekotorom klasse beskonechnoznachnykh analiticheskikh funktsii”, UMN, 74:2(446) (2019), 187–188  mathnet  crossref  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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