单频Schrodinger算子的absolutely continuous谱测度的Holder连续性
Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators
摘要：
本文在绝对连续谱区域内建立了具有丢番图频率的单频Schrodinger算子的谱测度分布的连续模的精确结果。更准确地说，我们建立了1/2-Holder连续几乎可约能量附近（绝对连续谱的一个必要支撑）。对于非微扰小的潜力（和几乎马蒂厄运营商与亚临界耦合），我们的结果适用于所有的能量。
英文摘要：
We establish sharp results on the modulus of continuity of the distribution of the spectral measure for one-frequency Schrodinger operators with Diophantine frequencies in the region of absolutely continuous spectrum. More precisely, we establish 1/2-Holder continuity near almost reducible energies (an essential support of absolutely continuous spectrum). For non-perturbatively small potentials (and for the almost Mathieu operator with subcritical coupling), our results apply for all energies.
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