标题： 量子图上预解算子和散射共振的等价性 显示英文标题

标题： Equivalence of resolvent and scattering resonances on quantum graphs

摘要： 我们讨论由有限紧致部分和有限个半直线组成的度量图上的Schrödinger算子的共振；假设顶点耦合为$\delta$型或其某些修改形式。 通过在图上使用外部复数缩放，我们证明在这种情况下，预解式和散射共振是一致的。 显示英文摘要

摘要： We discuss resonances for Schr\"odinger operators on metric graphs which consists of a finite compact part and a finite number of halflines attached to it; the vertex coupling is assumed to be of the $\delta$-type or certain modifications of it. Using exterior complex scaling on the graph we show that the resolvent and scattering resonances coincide in this case.