Essential spectrum of the discrete Laplacian on a perturbed periodic graph

被引：15

作者：

Sasaki, Itaru ^{[1
]}

Suzuki, Akito ^{[2
]}

机构：

[1] Shinshu Univ, Fac Sci, Dept Math Sci, Asahi Ku, Matsumoto, Nagano 3908621, Japan

[2] Shinshu Univ, Fac Engn, Div Math & Phys, Wakasato, Nagano 3808553, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 446卷 / 02期

关键词：

Infinite graph; Essential spectrum; Perturbation theory; Discrete Laplacian; Pendant; Random graph; SCHRODINGER-OPERATORS; INFINITE GRAPH; LATTICES;

D O I：

10.1016/j.jmaa.2016.09.063

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：1863 / 1881

页数：19

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