论文标题
$δ$束运算符的手术转换和光谱估计值
Surgery transformations and spectral estimates of $δ$ beam operators
论文作者
论文摘要
我们在公制图上引入了$δ$类型的顶点条件，即第四个导数操作员，并研究该图的某些几何变化（图形手术）对光束操作员光谱对紧凑型公制图的效果。对于一类顶点条件，可以将结果视为量子图的δ顶点条件的类似物。梁操作员有许多可能的δ类型条件候选物。我们制定手术原理并记录频谱的单调性特性，以期在某些图形变化后，顶点条件可能会在同一类内发生变化的可能性。我们还通过在特征值上获得几个高层和上层估计来证明手术原理的应用。
We introduce $δ$ type vertex conditions for beam operators, the fourth derivative operator, on metric graphs and study the effect of certain geometrical alterations (graph surgery) of the graph on the spectra of beam operators on compact metric graphs. Results are obtained for a class of vertex conditions which can be seen as an analogue of δ vertex conditions for quantum graphs. There are a number of possible candidates of δ type conditions for beam operators. We develop surgery principles and record the monotonicity properties of the spectrum, keeping in view the possibility that vertex conditions may change within the same class after certain graph alterations. We also demonstrate the applications of surgery principles by obtaining several lower and upper estimates on the eigenvalues.
