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

  • Leonid B. Golinskii

    B. Verkin Institute for Low Temperature Physics, Kharkiv, Ukraine
On stability in the Borg–Hochstadt theorem for periodic Jacobi matrices cover

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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 two-sided bounds between oscillations of the matrix entries along the diagonals and the length of the maximal gap in the spectrum.

Cite this article

Leonid B. Golinskii, On stability in the Borg–Hochstadt theorem for periodic Jacobi matrices. J. Spectr. Theory 9 (2019), no. 4, pp. 1507–1521

DOI 10.4171/JST/288