Essential spectrum of the discrete Laplacian on a perturbed periodic graph

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Sasaki, Itaru¹  Suzuki, Akito² 

[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

关键词: Infinite graph;    Essential spectrum;    Perturbation theory;    Discrete Laplacian;    Pendant;    Random graph;   

DOI  :  10.1016/j.jmaa.2016.09.063

来源: Elsevier

【 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.

【 授权许可】

Free