论文标题
多频Schrödinger操作员的零度量频谱
Zero Measure Spectrum for Multi-Frequency Schrödinger Operators
论文作者
论文摘要
勒贝格（Lebesgue）几乎每次翻译都以berthé的作品为基础 - 斯坦纳（Steiner） - 斯泰恩（Steiner） - 乌斯瓦尔德纳（Thuswaldner）和福格（Fogg），几乎每次翻译都承认了自然编码，因此相关的子迁移满足了Boshernitzan的标准。结果，我们表明，对于这些圆环翻译，每个准周期电位都可以通过相关的schrödinger运算符具有零lebesgue度量的cantor频谱均匀地近似。我们还描述了一个框架，该框架可以扩展到更高维的托里。
Building on works of Berthé--Steiner--Thuswaldner and Fogg--Nous we show that on the two-dimensional torus, Lebesgue almost every translation admits a natural coding such that the associated subshift satisfies the Boshernitzan criterion. As a consequence we show that for these torus translations, every quasi-periodic potential can be approximated uniformly by one for which the associated Schrödinger operator has Cantor spectrum of zero Lebesgue measure. We also describe a framework that can allow this to be extended to higher-dimensional tori.
