由区间交换变换定义的薛定谔算子
Schrödinger Operators Defined by Interval Exchange Transformations
摘要：
本文讨论了离散的一维薛定谔算子，其位势由紧致度量空间和连续实值采样函数的可逆遍历变换生成。我们特别注意的情况下，变换是一个最小的区间交换变换。建立了这些算子的谱和谱型的结果。特别是，我们提供了第一个例子的转换，相关的薛定谔算子有纯粹的奇异谱的每一个非常数连续采样函数。
英文摘要：
We discuss discrete one-dimensional Schrödinger operators whose potentials are generated by an invertible ergodic transformation of a compact metric space and a continuous real-valued sampling function. We pay particular attention to the case where the transformation is a minimal interval exchange transformation. Results about the spectrum and the spectral type of these operators are established. In particular, we provide the first examples of transformations for which the associated Schrödinger operators have purely singular spectrum for every non-constant continuous sampling function.
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