量子图中一般奇异点耦合的逼近
Approximation of a general singular vertex coupling in quantum graphs
摘要：
解决了量子图中所有奇异点耦合的近似问题。我们提出了一种结构，其中的边缘是解耦的，每对端点连接的边缘携带一个$δ$潜在的和一个矢量的潜在耦合到“松散”的边缘由$δ$耦合。它表明，如果连接边的长度收缩到零和潜力是适当的缩放，限制可以产生任何规定的奇异顶点耦合，而且，这样的近似收敛在范数预解式意义下。
英文摘要：
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a $δ$ potential and a vector potential coupled to the "loose" edges by a $δ$ coupling. It is shown that if the lengths of the connecting edges shrink to zero and the potentials are properly scaled, the limit can yield any prescribed singular vertex coupling, and moreover, that such an approximation converges in the norm-resolvent sense.
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