Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Solis, Moises Gomez
Institution: Louisiana State University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7222265878