矩阵势具有一阶矩的直线上离散薛定谔算子的Levinson定理

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2022-11-09 DOI:10.1142/s0219199723500177

M. Ballesteros, Gerardo Franco C'ordova, I. Naumkin, H. Schulz-Baldes

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引用次数: 0

摘要

本文证明了离散线上矩阵值Schr\ odinger算子的谱和散射理论的新结果，该算子具有非紧支持微扰，其第一阶矩假定存在。特别地，证明了Levinson定理，导出了散射数据与相应哈密顿量的谱性质(束缚态和半束缚态)之间的关系。该证明基于平稳散射理论，突出地使用了由volterra型积分方程控制的复能量处的Jost解。

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Levinson theorem for discrete Schrodinger operators on the line with matrix potentials having a first moment

This paper proves new results on spectral and scattering theory for matrix-valued Schr\"odinger 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.

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来源期刊

Communications in Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.