On stability in the Borg--Hochstadt theorem for periodic Jacobi matrices
Spectral Theory
2017-04-13 v1
Abstract
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 the two-sided bounds between oscillations of the matrix entries along the diagonals and the length of the maximal gap in the spectrum.
Keywords
Cite
@article{arxiv.1704.03679,
title = {On stability in the Borg--Hochstadt theorem for periodic Jacobi matrices},
author = {L. Golinskii},
journal= {arXiv preprint arXiv:1704.03679},
year = {2017}
}
Comments
11 pages in LaTeX