PreprintCC BY 4.0arXiv
A note on the A.C. spectrum of limit-periodic Jacobi matrices
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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BibTeX
@misc{solis2026note,
title = {{A note on the A.C. spectrum of limit-periodic Jacobi matrices}},
author = {Moises Gomez Solis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.19416},
eprint = {2610.19416},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.19416},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A note on the A.C. spectrum of limit-periodic Jacobi matrices
AU - Moises Gomez Solis
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.19416
UR - https://arxiv.org/abs/2610.19416
AB - 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.
ER -