论文标题
局部模块框架和来自Groperoid Morita等效的底座
Localised module frames and Wannier bases from groupoid Morita equivalences
论文作者
论文摘要
遵循操作员的代数方法进行Gabor分析，我们构建了翻译框架，以用于Hilbert空间的位置，莫里塔等效性双模块是由hausdorff gropsoids之间的类固醇等效性产生的，其中一组类别类型是eétaleofétale和一个紧凑的单位空间。对于有限生成和投射的子模块，我们显示这些帧是正统的，并且仅当模块是免费的。然后，我们将此结果应用于Schrödinger运算符光谱子空间的局部Wannier底座，该子空间具有（Aperiodic）Delone集的原子电位。非交换性的Chern数量为快速付费的降水底座提供了拓扑障碍，我们表明，在基础DeLone集合的变形下，该结果稳定。
Following the operator algebraic approach to Gabor analysis, we construct frames of translates for the Hilbert space localisation of the Morita equivalence bimodule arising from a groupoid equivalence between Hausdorff groupoids, where one of the groupoids is étale and with a compact unit space. For finitely generated and projective submodules, we show these frames are orthonormal bases if and only if the module is free. We then apply this result to the study of localised Wannier bases of spectral subspaces of Schrödinger operators with atomic potentials supported on (aperiodic) Delone sets. The noncommutative Chern numbers provide a topological obstruction to fast-decaying Wannier bases and we show this result is stable under deformations of the underlying Delone set.
