可微拟周期Schr dinger算子的absolutely continuous谱
The absolutely continuous spectrum of finitely differentiable quasi-periodic Schrödinger operators
摘要：
本文证明了具有可微势的拟周期薛定谔算子在相应的$C^k$拓扑中，若频率为丢番图且势足够小，则其所有相位都具有纯绝对连续谱.这是基于一个精炼的定量$C^{k,k_0}$几乎约化定理，它只需要一个相当低的初始正则性"$k>14τ+2$"，并且大部分正则性"$k_0\leq k-2τ-2$"在最后是守恒的，其中$τ$是频率的丢番图常数。
英文摘要：
We prove that the quasi-periodic Schrödinger operator with a finitely differentiable potential has purely absolutely continuous spectrum for all phases if the frequency is Diophantine and the potential is sufficiently small in the corresponding $C^k$ topology. This is based on a refined quantitative $C^{k,k_0}$ almost reducibility theorem which only requires a quite low initial regularity ``$k>14τ+2$'' and much of the regularity ``$k_0\leq k-2τ-2$'' is conserved in the end, where $τ$ is the Diophantine constant of the frequency.
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