论文标题
关于珀森的公式；典型的群体方法
On Persson's Formula; an Étale Groupoid Approach
论文作者
论文摘要
Persson的公式在$ r^n $中表达了合适的自动偶像施罗丁格操作员的基本频谱，就操作员限制家族的较低频谱点而言，以相对紧凑的子集的补充。它已扩展到其他情况。我们提出了一种基于$ c^*$ - 与étalegroupoid相关的代数的方法。在这种情况下，有固有的版本，指的是groupoid $ c^*$ - 代数的自动伴侣元素。当考虑希尔伯特空间中的表示时，结果并不总是涉及必需频谱。应用程序的范围与传统应用完全不同。我们指出了与符号动力学有关的示例，并且在离散度量空间上以频带为主导的操作员。治疗只需要少量的对称性。即使涉及小组行动，也需要限制非变变子集，必须仔细治疗。
Persson's formula expresses the infimum of the essential spectrum of a suitable self-adjoint Schrödinger operator in $R^n$ in terms of the lower spectral points of a family of restrictions of the operator to complements of relatively compact subsets. It has been extended to other situations. We present an approach based on $C^*$-algebras associated to étale groupoids. In such a setting there are intrinsic versions, referring to self-adjoint elements of the groupoid $C^*$-algebras. When representations in Hilbert spaces are considered, the results not always involve only the essential spectrum. The range of applications is quite distinct from the traditional one. We indicate examples related to symbolic dynamics and band dominated operators on discrete metric spaces. The treatment needs only a small amount of symmetry. Even when group actions are involved, restrictions to non-invariant subsets are needed and have to be treated carefully.
