Resolvent expansion for the Schrodinger operator on a graph with infinite rays
Resolvent expansion for the Schrodinger operator on a graph with infinite rays
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无限射线图上薛定谔算子的解析展开
DOI：
10.1016/j.jmaa.2018.04.022
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发表时间：
2018
影响因子：
1.3
通讯作者：
Arne Jensen
中科院分区：
文献类型：
--
作者：
Kenichi Ito;Arne Jensen
我们考虑由有限图和有限数量的离散半直线组成的组合图上的薛定谔算子，所有连接在一起，并计算其预解式在阈值0附近的渐近展开。精确的表达式获得的前几个系数的广义本征函数的扩展。这一结果证明了阈值类型的分类仅由广义本征函数的增长特性。通过选择一个不具有零本征值或零共振的自由算子，我们可以使展开过程简化到与单离散半直线上的展开过程相同的程度。
We consider the Schrödinger operator on a combinatorial graph consisting of a finite graph and a finite number of discrete half-lines, all jointed together, and compute an asymptotic expansion of its resolvent around the threshold 0. Precise expressions are obtained for the first few coefficients of the expansion in terms of the generalized eigenfunctions. This result justifies the classification of threshold types solely by growth properties of the generalized eigenfunctions. By choosing an appropriate free operator a priori possessing no zero eigenvalue or zero resonance we can simplify the expansion procedure as much as that on the single discrete half-line.