English

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}
}

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11 pages in LaTeX