离散图的内外对偶
Exterior-Interior Duality for Discrete Graphs
摘要：
外部-内部对偶性表达了$\mathbb{R}^2$中有界连通区域上的Laplace谱与区域外部的散射矩阵之间的深层联系。在这里，这个链接扩展到有限图上的离散拉普拉斯算子的谱的研究。为此，设计了两种方法，用于关联散射矩阵的图形。这两种方法的外部-内部的对偶性。
英文摘要：
The Exterior-Interior duality expresses a deep connection between the Laplace spectrum in bounded and connected domains in $\mathbb{R}^2$, and the scattering matrices in the exterior of the domains. Here, this link is extended to the study of the spectrum of the discrete Laplacian on finite graphs. For this purpose, two methods are devised for associating scattering matrices to the graphs. The Exterior -Interior duality is derived for both methods.
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