THE SPECTRUM OF PERIODIC JACOBI MATRICES WITH SLOWLY OSCILLATING DIAGONAL TERMS

被引：1

作者：

Martinez, Carmen ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Fac Ciencias, Dept Matemat, Mexico City 04510, DF, Mexico

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2008年 / 51卷

关键词：

Jacobi matrices; orthogonal polynomials; spectrum;

D O I：

10.1017/S0013091505001070

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the spectrum of periodic Jacobi matrices. We concentrate on the case of slowly oscillating diagonal terms and study the behaviour of the zeros of the associated orthogonal polynomials in the spectral gap. We find precise estimates for the distance from single eigenvalues of truncated matrices in the spectral gap to the diagonal entries of the matrix. We include a brief numerical example to show the exactness of our estimates.

引用

页码：751 / 763

页数：13

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