Exact local distribution of the absolutely continuous spectral measure
Mathematical Physics
2024-07-15 v1 Dynamical Systems
math.MP
Spectral Theory
Abstract
It is well-established that the spectral measure for one-frequency Schr\"odinger operators with Diophantine frequencies exhibits optimal -H\"older continuity within the absolutely continuous spectrum. This study extends these findings by precisely characterizing the local distribution of the spectral measure for dense small potentials, including a notable result for any subcritical almost Mathieu operators. Additionally, we investigate the stratified H\"older continuity of the spectral measure at subcritical energies.
Keywords
Cite
@article{arxiv.2407.09278,
title = {Exact local distribution of the absolutely continuous spectral measure},
author = {Xianzhe Li and Jiangong You and Qi Zhou},
journal= {arXiv preprint arXiv:2407.09278},
year = {2024}
}
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49 pages