On stability in the Borg-Hochstadt theorem for periodic Jacobi matrices

被引：1

作者：

Golinskii, Leonid ^{[1
]}

机构：

[1] B Verkin Inst Low Temp Phys & Engn, 47 Nauky Ave, UA-61103 Kharkov, Ukraine

来源：

JOURNAL OF SPECTRAL THEORY | 2019年 / 9卷 / 04期

关键词：

Periodic Jacobi matrices; spectrum; bands and gaps; Hill discriminant; trace formulae;

D O I：

10.4171/JST/288

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A result of Borg-Hochstadt in the theory of periodic Jacobi matrices states that such a matrix has constant diagonals as long as all gaps in its spectrum are closed (have zero length). We suggest a quantitative version of this result by proving two-sided bounds between oscillations of the matrix entries along the diagonals and the length of the maximal gap in the spectrum.

引用

页码：1507 / 1521

页数：15

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