论文标题
Schrödinger操作员的Krein-Von Neumann扩展名公制图
The Krein-von Neumann extension for Schrödinger operators on metric graphs
论文作者
论文摘要
研究了Krein-von Neumann扩展名，用于用于公制图的Schrödinger操作员。除其他外，其顶点条件是明确表示的，并探讨了其与其他自我伴侣顶点条件（例如连续性-Kirchhoff）的关系。获得了其正征值的变分表征。基于此，研究了其特征值在公制图的扰动下的行为，并确定了所谓的手术原理。此外，还获得了等等特征值不平等。
The Krein-von Neumann extension is studied for Schrödinger operators on metric graphs. Among other things, its vertex conditions are expressed explicitly, and its relation to other self-adjoint vertex conditions (e.g. continuity-Kirchhoff) is explored. A variational characterisation for its positive eigenvalues is obtained. Based on this, the behaviour of its eigenvalues under perturbations of the metric graph is investigated, and so-called surgery principles are established. Moreover, isoperimetric eigenvalue inequalities are obtained.
