Jacobi matrices on trees generated by Angelesco systems: asymptotics of coefficients and essential spectrum
Spectral Theory
2022-02-01 v2 Classical Analysis and ODEs
Abstract
We continue studying the connection between Jacobi matrices defined on a tree and multiple orthogonal polynomials (MOPs) that was discovered previously by the authors. In this paper, we consider Angelesco systems formed by two analytic weights and obtain asymptotics of the recurrence coefficients and strong asymptotics of MOPs along all directions (including the marginal ones). These results are then applied to show that the essential spectrum of the related Jacobi matrix is the union of intervals of orthogonality.
Keywords
Cite
@article{arxiv.2004.04113,
title = {Jacobi matrices on trees generated by Angelesco systems: asymptotics of coefficients and essential spectrum},
author = {Alexander I. Aptekarev and Sergey A. Denisov and Maxim L. Yattselev},
journal= {arXiv preprint arXiv:2004.04113},
year = {2022}
}