A note on self-adjoint extensions of the Laplacian on weighted graphs

2012/08/31 by Xueping Huang, Huang, Xueping, Matthias Keller +5 · 2 citations
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1208.6358

openalex publication_date 2012/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on weighted graphs. We first show that, for locally finite graphs and a certain family of metrics, completeness of the graph implies uniqueness of these extensions. Moreover, in the case when the graph is not metrically complete and the Cauchy boundary has finite capacity, we characterize the uniqueness of the Markovian extensions.

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• Essential self-adjointness of non-semibounded Schrödinger operators on infinite graphs
• On Hodge Laplacians on General Simplicial Complexes

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