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

Title: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 $EC(\eta)$ have purely absolutely continuous spectral type when $\eta$ 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.

Spectral Theory (math.SP); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

arXiv:2610.19416 [math.SP]

(or arXiv:2610.19416v1 [math.SP] for this version)

https://doi.org/10.48550/arXiv.2610.19416 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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