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Uspekhi Mat. Nauk, 2017, Volume 72, Issue 3(435), Pages 3–64 (Mi umn9769)  

This article is cited in 8 scientific papers (total in 8 papers)

On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials

A. I. Aptekareva, G. López Lagomasinob, A. Martínez-Finkelshteinc

a Federal Research Centre Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
b Carlos III University of Madrid, Madrid, Spain
c Universidad de Almería, Almería, Spain

Abstract: This survey considers multiple orthogonal polynomials with respect to Nikishin systems generated by a pair $(\sigma_1,\sigma_2)$ of measures\linebreak with unbounded supports ($\operatorname{supp}(\sigma_1) \subseteq \mathbb{R}_+$, $\operatorname{supp}(\sigma_2)\subset \mathbb{R}_-$) and with $\sigma_2$ discrete. A Nikishin-type equilibrium problem in the presence of an external field acting on $\mathbb{R}_+$ and a constraint on $\mathbb{R}_-$ is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials.
Bibliography: 56 titles.

Keywords: Hermite–Padé approximants, multiple orthogonal polynomials, orthogonality with respect to a discrete measure, weak asymptotics, vector equilibrium problem, Nikishin systems.

Funding Agency Grant Number
Russian Science Foundation 14-21-00025п
European Regional Development Fund
Consejería Economía, Innovación, Ciencia y Empleo, Junta de Andalucía P11-FQM-7276
Ministerio de Economía y Competitividad MTM2015-65888-C4-2-P
Fundación CEI.Mar
The work of the first author was supported by a grant of the Russian Science Foundation (project no. 14-21-00025п). The second and the third authors were supported by MICINN of Spain (grant nos. MTM2015-65888-C4-2-P and MTM2011-28952-C02-01) and by the European Regional Development Fund, and the third author was also supported by Junta de Andalucía (the Excellence Grant P11-FQM-7276 and the research group FQM-229) and by Campus de Excelencia Internacional del Mar of the University of Almería.


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English version:
Russian Mathematical Surveys, 2017, 72:3, 389–449

Bibliographic databases:

UDC: 517.53
MSC: Primary 42C05; Secondary 31A99, 41A21
Received: 13.03.2017
Revised: 10.04.2017

Citation: A. I. Aptekarev, G. López Lagomasino, A. Martínez-Finkelshtein, “On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials”, Uspekhi Mat. Nauk, 72:3(435) (2017), 3–64; Russian Math. Surveys, 72:3 (2017), 389–449

Citation in format AMSBIB
\by A.~I.~Aptekarev, G.~L\'opez Lagomasino, A.~Mart{\'\i}nez-Finkelshtein
\paper On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials
\jour Uspekhi Mat. Nauk
\yr 2017
\vol 72
\issue 3(435)
\pages 3--64
\jour Russian Math. Surveys
\yr 2017
\vol 72
\issue 3
\pages 389--449

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    This publication is cited in the following articles:
    1. V. G. Lysov, “Silnaya asimptotika approksimatsii Ermita–Pade dlya sistemy Nikishina s vesami Yakobi”, Preprinty IPM im. M. V. Keldysha, 2017, 085, 35 pp.  mathnet  crossref
    2. V. G. Lysov, “Asymptotics of Jacobi–Piñeiro Polynomials and Functions of the Second Kind”, Math. Notes, 103:3 (2018), 495–498  mathnet  crossref  crossref  isi  elib
    3. E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. I. Aptekarev, E. D. Belega, “Asymptotic behaviour of the information entropy of hydrogen-like quantum systems”, Russian Math. Surveys, 73:5 (2018), 922–924  mathnet  crossref  crossref  adsnasa  isi  elib
    5. E. M. Chirka, “Potentials on a compact Riemann surface”, Proc. Steklov Inst. Math., 301 (2018), 272–303  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    6. A. I. Aptekarev, Yu. G. Rykov, “Variational principle for multidimensional conservation laws and pressureless media”, Russian Math. Surveys, 74:6 (2019), 1117–1119  mathnet  crossref  crossref  adsnasa  isi
    7. A. I. Aptekarev, M. A. Lapik, V. G. Lysov, “Direct and inverse problems for vector logarithmic potentials with external fields”, Anal. Math. Phys., 9:3 (2019), 919–935  crossref  mathscinet  zmath  isi  scopus
    8. I. A. Aptekarev, S. A. Denisov, M. L. Yattselev, “Self-adjoint Jacobi matrices on trees and multiple orthogonal polynomials”, Trans. Amer. Math. Soc., 373:2 (2020), 875–917  crossref  mathscinet  zmath  isi  scopus
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