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arXiv · 1704.03679

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

L. Golinskii
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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.

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L. Golinskii. 2017-04-12. On stability in the Borg--Hochstadt theorem for periodic Jacobi matrices. https://arxiv.org/abs/1704.03679

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