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.
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页码：1507 / 1521
页数：15
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