Jacobi matrices on trees generated by Angelesco systems: asymptotics of coefficients and essential spectrum

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2020-04-08 DOI:10.4171/jst/380

A. Aptekarev, S. Denisov, M. Yattselev

引用次数: 5

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.

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Angelesco系统生成树上的Jacobi矩阵：系数和本质谱的渐近性

我们继续研究树上定义的雅可比矩阵与作者先前发现的多个正交多项式（MOP）之间的联系。本文考虑由两个分析权组成的Angelesco系统，得到了递推系数的渐近性和MOP沿所有方向（包括边缘方向）的强渐近性。然后应用这些结果证明了相关雅可比矩阵的本质谱是正交性区间的并集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.