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arXiv · 2610.19416

A note on the A.C. spectrum of limit-periodic Jacobi matrices

Moises Gomez Solis
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Abstract

We show that limit-periodic Jacobi matrices in the weak exponential class $EC(η)$ have purely absolutely continuous spectral type when $η$ is sufficiently large, depending only on the $R$-boundedness constant. The proof first establishes homogeneity of the spectrum from the weak exponential approximation rate. A closure theorem for reflectionless Jacobi matrices then transfers reflectionlessness from the periodic approximants to the limit, and a theorem of Poltoratski and Remling rules out singular spectrum on a homogeneous set.

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Moises Gomez Solis. 2026-10-14. A note on the A.C. spectrum of limit-periodic Jacobi matrices. https://arxiv.org/abs/2610.19416

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