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

A. I. Aptekarev; G. López Lagomasino; A. Martínez-Finkelshtein

doi:10.1070/RM9769

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

A. I. Aptekarev, G. López Lagomasino, A. Martínez-Finkelshtein

Research output: Contribution to journal › Review article › peer-review

9 Scopus citations

Abstract

This survey considers multiple orthogonal polynomials with respect to Nikishin systems generated by a pair (σ₁, σ₂) of measures with unbounded supports (supp(σ₁) ⊂ R₊, supp(σ₂) ⊂R_-) and with σ₂ discrete. A Nikishin-type equilibrium problem in the presence of an external field acting on R+ and a constraint on R- is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials.

Original language	English
Pages (from-to)	389-449
Number of pages	61
Journal	Russian Mathematical Surveys
Volume	72
Issue number	3
DOIs	https://doi.org/10.1070/RM9769
State	Published - 1 Jan 2017
Externally published	Yes

Keywords

Hermite-Padé approximants
Multiple orthogonal polynomials
Nikishin systems
Orthogonality with respect to a discrete measure
Vector equilibrium problem
Weak asymptotics

ASJC Scopus subject areas

General Mathematics

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10.1070/RM9769

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title = "On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials",

abstract = "This survey considers multiple orthogonal polynomials with respect to Nikishin systems generated by a pair (σ1, σ2) of measures with unbounded supports (supp(σ1) ⊂ R+, supp(σ2) ⊂R-) and with σ2 discrete. A Nikishin-type equilibrium problem in the presence of an external field acting on R+ and a constraint on R- is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials.",

keywords = "Hermite-Pad{\'e} approximants, Multiple orthogonal polynomials, Nikishin systems, Orthogonality with respect to a discrete measure, Vector equilibrium problem, Weak asymptotics",

author = "Aptekarev, {A. I.} and {L{\'o}pez Lagomasino}, G. and A. Mart{\'i}nez-Finkelshtein",

note = "Publisher Copyright: {\textcopyright} 2017 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd.",

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doi = "10.1070/RM9769",

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T1 - On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials

AU - Aptekarev, A. I.

AU - López Lagomasino, G.

AU - Martínez-Finkelshtein, A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - This survey considers multiple orthogonal polynomials with respect to Nikishin systems generated by a pair (σ1, σ2) of measures with unbounded supports (supp(σ1) ⊂ R+, supp(σ2) ⊂R-) and with σ2 discrete. A Nikishin-type equilibrium problem in the presence of an external field acting on R+ and a constraint on R- is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials.

AB - This survey considers multiple orthogonal polynomials with respect to Nikishin systems generated by a pair (σ1, σ2) of measures with unbounded supports (supp(σ1) ⊂ R+, supp(σ2) ⊂R-) and with σ2 discrete. A Nikishin-type equilibrium problem in the presence of an external field acting on R+ and a constraint on R- is stated and solved. The solution is used for deriving the contracted zero distribution of the associated multiple orthogonal polynomials.

KW - Hermite-Padé approximants

KW - Multiple orthogonal polynomials

KW - Nikishin systems

KW - Orthogonality with respect to a discrete measure

KW - Vector equilibrium problem

KW - Weak asymptotics

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U2 - 10.1070/RM9769

DO - 10.1070/RM9769

M3 - Review article

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VL - 72

SP - 389

EP - 449

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

IS - 3

ER -

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

Abstract

Keywords

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