English

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

Classical Analysis and ODEs 2020-04-13 v2 Mathematical Physics math.MP Spectral Theory

Abstract

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 equation becomes ordinary. For Angelesco systems, the result is illustrated numerically.

Keywords

Cite

@article{arxiv.1908.04540,
  title  = {Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class},
  author = {Alexander I. Aptekarev and Rostyslav Kozhan},
  journal= {arXiv preprint arXiv:1908.04540},
  year   = {2020}
}

Comments

21 pages; 2 figures

R2 v1 2026-06-23T10:46:04.544Z