The Adjacency Matrix and the Discrete Laplacian Acting on Forms

被引：0

作者：

Hatem Baloudi

Sylvain Golénia

Aref Jeribi

机构：

[1] Faculté Des Sciences De Sfax,

[2] Univ. Bordeaux,undefined

[3] Bordeaux INP,undefined

[4] CNRS,undefined

[5] IMB,undefined

[6] UMR 5251,undefined

来源：

Mathematical Physics, Analysis and Geometry | 2019年 / 22卷

关键词：

Discrete Laplacian; Locally finite graphs; Self-adjoint extension; Adjacency matrix; Forms; 81Q35; 47B25; 05C63;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We complete the understanding of the question of the essential self-adjoitness and non-essential self-adjointness of the discrete Laplacian acting on 1-forms. We also discuss the notion of completeness. Moreover, we study the relationship between the adjacency matrix of the line graph and the discrete Laplacian acting on 1-forms. Thanks to it, we exhibit a condition that ensures that the adjacency matrix on line graph is bounded from below and not essentially self-adjoint.

引用

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