可平面图上本征函数的Eigenvalue渐近性和唯一延拓性
Eigenvalue asymptotics and unique continuation of eigenfunctions on planar graphs
摘要：
研究了有限集外具有大负曲率的可平面图及其上Schr{}dinger算子的谱理论.我们得到了特征值渐近性的一阶和二阶估计。此外，我们还证明了本征函数的唯一延拓结果和一般本征函数的衰减性质。的证明依赖于一个详细的分析几何采用复制和粘贴程序的基础上的Gaussian-Bonnet定理。
英文摘要：
We study planar graphs with large negative curvature outside of a finite set and the spectral theory of Schr{ö}dinger operators on these graphs. We obtain estimates on the first and second order term of the eigenvalue asymptotics. Moreover, we prove a unique continuation result for eigenfunctions and decay properties of general eigenfunctions. The proofs rely on a detailed analysis of the geometry which employs a Copy-and-Paste procedure based on the Gauß-Bonnet theorem.
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