Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class

JOURNAL OF APPROXIMATION THEORY

卷:255

Article

Aptekarev, Alexander, I¹  Kozhan, Rostyslav² 

[1] Russian Acad Sci, Keldysh Inst Appl Math, Miusskaya Pl 4, Moscow 125047, Russia

[2] Uppsala Univ, Box 480, Uppsala 75106, Sweden

关键词: Multiple orthogonality;    Recurrence coefficients;    Angelesco systems;   

DOI  :  10.1016/j.jat.2020.105409

来源: Elsevier

【 摘 要 】

A limiting property of the nearest-neighbor recurrence coefficients for multiple orthogonal polynomials from a Nevai class is investigated. Namely, assuming that the nearest-neighbor coefficients have a limit along rays of the lattice, we describe it in terms of the solution of a system of partial differential equations. In the case of two orthogonality measures the differential equations become ordinary. For Angelesco systems, the result is illustrated numerically. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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