AN EQUILIBRIUM PROBLEM FOR THE LIMITING EIGENVALUE DISTRIBUTION OF RATIONAL TOEPLITZ MATRICES

被引：6

作者：

Delvaux, Steven ^{[1
]}

Duits, Maurice ^{[2
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, B-3001 Louvain, Belgium

[2] CALTECH, Dept Math, Pasadena, CA 91125 USA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2010年 / 31卷 / 04期

关键词：

Toeplitz matrix; rational function; generalized eigenvalues; (vector) potential theory; EXPANSION;

D O I：

10.1137/090778468

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit of the normalized eigenvalue counting measure is a particular component of the unique solution to a vector equilibrium problem. Moreover, we show that the other components describe the limiting behavior of certain generalized eigenvalues. In this way, we generalize recent results by Kuijlaars and one of the authors [SIAM J. Matrix Anal. Appl., 30 (2008), pp. 173-196] that were concerned with banded Toeplitz matrices.

引用

页码：1894 / 1914

页数：21

共 16 条

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[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2008, 30 (01) : 173 - 196
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