The adjacency matrix and the discrete Laplacian acting on forms

2015/05/22 by Baloudi, Hatem, Golenia, Sylvain, Jeribi, Aref · 4 citations
#FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1505.06109

Abstract

We study the relationship between the adjacency matrix and the discrete Laplacian acting on 1-forms. We also prove that if the adjacency matrix is bounded from below it is not necessarily essentially self-adjoint. We discuss the question of essential self-adjointness and the notion of completeness.

Cited by

• Hodge Laplacians on Weighted Simplicial Complexes: Forms, Closures, and Essential Self-Adjointness
• Geometric Criteria for Essential Self-Adjointness of Discrete Hodge Laplacians on Weighted Simplicial Complexes
• Essential self-adjointness of non-semibounded Schrödinger operators on infinite graphs
• On Hodge Laplacians on General Simplicial Complexes

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