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.
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