具有纯奇异谱的Stark-Wannier型算子
Stark-Wannier type operators with purely singular spectrum
摘要：
考虑一维Stark-Wannier型算子，其位势由无穷远处对数增长的光滑函数加上傅立叶系数为$(\ln |n|)^{-b}, 0<b<1/2$的周期函数给出.我们证明了在有理电场的情况下，相应算子的谱是纯奇异连续的。
英文摘要：
We consider the one-dimensional Stark-Wannier type operators with potentials given by a smooth function with a logarithmic growth at infinity plus a periodic function with the Fourier coefficients of the form $(\ln |n|)^{-b}, 0<b<1/2$. We prove that in the case of rational electric field the spectrum of the corresponding operator is purely singular continuous.
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