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

2017/04/12 by Leonid Golinskiĭ, L. Golinskii, Golinskii, L.
Computer Science · Materials Science · Mathematics · #47B36 #FOS: Mathematics #Magnetism in coordination complexes #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP #msc:47B36

paper · pdf · doi:10.48550/arxiv.1704.03679

11 pages in LaTeX

arxiv created 2017/04/12 · openalex publication_date 2017/04/12 · arxiv updated 2017/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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