微扰拓扑晶体上薛定谔算子的谱和散射理论
Spectral and scattering theory for Schrödinger operators on perturbed topological crystals
摘要：
本文研究了薛定谔算子作用在扰动周期离散图上的谱理论和散射理论。考虑的扰动有两种类型：无论是一个乘法算子的短程或长程功能，或短程型修改的顶点和边缘上的图定义的措施。谱理论用于描述基本算子的谱的性质。对于短程扰动，也证明了局域波算子的存在性和完备性。
英文摘要：
In this paper we investigate the spectral and the scattering theory of Schrödinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or a long-range function, or a short-range type modification of the measure defined on the vertices and on the edges of the graph. Mourre theory is used for describing the nature of the spectrum of the underlying operators. For short-range perturbations, existence and completeness of local wave operators are also proved.
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