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This article is cited in 5 scientific papers (total in 5 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.
DOI:
https://doi.org/10.4213/rm9769
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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
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http://mi.mathnet.ru/eng/umn9769https://doi.org/10.4213/rm9769 http://mi.mathnet.ru/eng/umn/v72/i3/p3
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V. G. Lysov, “Silnaya asimptotika approksimatsii Ermita–Pade dlya sistemy Nikishina s vesami Yakobi”, Preprinty IPM im. M. V. Keldysha, 2017, 085, 35 pp.
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V. G. Lysov, “Asymptotics of Jacobi–Piñeiro Polynomials and Functions of the Second Kind”, Math. Notes, 103:3 (2018), 495–498
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E. A. Rakhmanov, “Zero distribution for Angelesco Hermite–Padé polynomials”, Russian Math. Surveys, 73:3 (2018), 457–518
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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
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E. M. Chirka, “Potentials on a compact Riemann surface”, Proc. Steklov Inst. Math., 301 (2018), 272–303
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