The eigenvalues of the Laplacian on locally finite networks

被引：0

作者：

von Below J. ^{[1
]}

Lubary J.A. ^{[2
]}

机构：

[1] LMPA Joseph Liouville, EA 2597, Université du Littoral Côte d’Opale, 50, rue F. Buisson, B.P. 699, Calais Cedex

[2] Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Campus Nord, Edifici Ω, Jordi Girona, 1-3, Barcelona

来源：

Results in Mathematics | 2005年 / 47卷 / 3-4期

关键词：

05C10; 05C50; 34B45; 34L10; 35J05; 35P10; adjacency and transition operator; eigenvalue problems; Laplacian; Locally finite graphs and networks;

D O I：

10.1007/BF03323026

中图分类号：

学科分类号：

摘要：

We consider the continuous Laplacian on an infinite locally finite network with equal edge lengths under natural transition conditions as continuity at the ramification nodes and classical Kirchhoff conditions at all vertices. It is shown that eigenvalues of the Laplacian in a L∞-setting are closely related to those of the adjacency and transition operator of the network. In this way the point spectrum is determined completely in terms of combinatorial quantities and properties of the underlying graph as in the finite case [2]. Moreover, the occurrence of infinite geometric multiplicity on trees and some periodic graphs is investigated. © 2005, Birkhäuser Verlag, Basel.

引用

页码：199 / 225

页数：26

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