SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 386-434, January 2021.
We study the reducibility of a linear Schrodinger equation subject to a small unbounded almost periodic perturbation which is analytic in time and space. Under appropriate assumptions on the smallness, analyticity, and on the frequency of the almost periodic perturbation, we prove that such an equation is reducible to constant coefficients via an analytic almost periodic change of variables. This implies control of both Sobolev and analytic norms for the solution of the corresponding Schrödinger equation for all times.

中文翻译：

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具有几乎周期电势的线性Schrödinger方程

SIAM数学分析杂志，第53卷，第1期，第386-434页，2021年1月。
我们研究线性Schrodinger方程的可约性，该线性Schrodinger方程受到小的无界几乎是周期性的扰动，这是时空分析的结果。在关于小度，解析度和几乎周期性扰动的频率的适当假设下，我们证明了通过对变量进行近似周期性的分析，该方程可简化为常数系数。这意味着始终要控制Sobolev和解析范数以求解相应的Schrödinger方程。