Distribution of eigenvalues of Toeplitz matrices with smooth entries

被引：2

作者：

Lubinsky, D. S. ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2022年 / 633卷

关键词：

Toeplitz matrices; Eigenvalue distribution; SERIES; CONJECTURE; CRITERIA; ROWS;

D O I：

10.1016/j.laa.2021.10.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate distribution of eigenvalues of growing size Toeplitz matrices [a(n+k-j)](1 <= j,k <= n) as n -> infinity, when the entries {a(j)} are "smooth" in the sense, for example, that for some alpha > 0, a(j-1)a(j+1)/a(j)(2) = 1 - 1/a(j) (1 + o(1)), j -> infinity. Typically they are Maclaurin series coefficients of an entire function. We establish that when suitably scaled, the eigenvalue counting measures have limiting support on [0,1], and under mild additional smoothness conditions, the universal scaled and weighted limit distribution is vertical bar pi logt vertical bar(-1/2) dt on [0,1]. (C) 2021 Elsevier Inc. All rights reserved.

引用

页码：332 / 365

页数：34