度量图上薛定谔算子的Krein-von Neumann扩张
The Krein-von Neumann extension for Schrödinger operators on metric graphs
摘要：
研究了度量图上薛定谔算子的Krein-von Neumann扩张。除此之外，它的顶点条件明确表示，并探讨其与其他自伴顶点条件（例如连续性-基尔霍夫）的关系。得到了其正特征值的变分特征。在此基础上，研究了其特征值在度量图扰动下的行为，建立了所谓的外科手术原理。此外，还得到了等周特征值不等式。
英文摘要：
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.
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