论文标题
Levinson定理用于离散的Schrödinger操作员，矩阵电势具有第一刻
Levinson theorem for discrete Schrödinger operators on the line with matrix potentials having a first moment
论文作者
论文摘要
本文证明了矩阵值schrödinger运算符在离散线上的频谱和散射理论的新结果，并以非紧密支撑的扰动为基础，假定其暂时存在。特别地，证明了列文森定理，其中得出了相应的汉密尔顿人的散射数据与光谱特性（绑定和半结合状态）之间的关系。该证明是基于固定散射理论的，其在复杂能量上明显地使用了由Volterra型积分方程控制的复杂能。
This paper proves new results on spectral and scattering theory for matrix-valued Schrödinger operators on the discrete line with non-compactly supported perturbations whose first moments are assumed to exist. In particular, a Levinson theorem is proved, in which a relation between scattering data and spectral properties (bound and half bound states) of the corresponding Hamiltonians is derived. The proof is based on stationary scattering theory with prominent use of Jost solutions at complex energies that are controlled by Volterra-type integral equations.
