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

2014/03/15 by Alexander Ivanovich Aptekarev, Aptekarev, A. I., G. López Lagomasino +3 · 1 citation
Mathematics · #30E10 #41A20 #42C05 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1403.3729

openalex publication_date 2014/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider multiple orthogonal polynomials with respect to Nikishin systems generated by two measures (σ₁, σ₂) with unbounded supports (supp σ₁ ⊆ ℝ₊, supp σ₂ ⊆ ℝ_-) and σ₂ is 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.

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• Scalar approaches to the limit distribution of the zeros of Hermite-Pade polynomials for a Nikishin system

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