图Laplacian的迹公式及其在匹配条件恢复中的应用
Trace formulae for graph Laplacians with applications to recovering matching conditions
摘要：
在图的顶点匹配条件为$δ$型或$δ'$型的假设下，研究了有限紧度量图上的图拉普拉斯算子.在这两种情况下，一个无限系列的迹公式连接在一起的两个不同的图拉普拉斯，只要他们的谱重合。给出了基于图拉普拉斯算子谱的匹配条件重构问题的应用。
英文摘要：
Graph Laplacians on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of either $δ$ or $δ'$ type. In either case, an infinite series of trace formulae which link together two different graph Laplacians provided that their spectra coincide is derived. Applications are given to the problem of reconstructing matching conditions for a graph Laplacian based on its spectrum.
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