Essential spectrum of the discrete Laplacian on a perturbed periodic graph
Essential spectrum of the discrete Laplacian on a perturbed periodic graph
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扰动周期图上离散拉普拉斯算子的基本谱
DOI：
10.1016/j.jmaa.2016.09.063
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发表时间：
2017
影响因子：
1.3
通讯作者：
Akito Suzuki
中科院分区：
文献类型：
--
作者：
Itaru Sasaki;Akito Suzuki
我们讨论了扰动周期图上的拉普拉斯算子，而扰动周期图可能不是周期图。给出了扰动图上Laplacian的本质谱包含未扰动图上Laplacian的本质谱的一个判据。该准则适用于一类由非紧扰动（如添加或删除无穷多个顶点和边）得到的图。使用这个标准，我们演示了如何确定锥状图，上半平面，并从Z 2通过随机添加顶点得到的图的谱。
We address the Laplacian on a perturbed periodic graph which might not be a periodic graph. We give a criterion for the essential spectrum of the Laplacian on the perturbed graph to include that on the unperturbed graph. This criterion is applicable to a wide class of graphs obtained by a non-compact perturbation such as adding or removing infinitely many vertices and edges. Using this criterion, we demonstrate how to determine the spectra of cone-like graphs, the upper-half plane, and graphs obtained from Z 2 by randomly adding vertices.