Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity
Functional Analysis
2024-04-22 v1
Abstract
We give two characterizations for the essential self-adjointness of the weighted Laplacian on birth-death chains. The first involves the edge weights and vertex measure and is classically known; however, we give another proof using stability results, limit point-limit circle theory and the connection between essential self-adjointness and harmonic functions. The second characterization involves a new notion of capacity. Furthermore, we also analyze the essential self-adjointness of Schr\"odinger operators, use the characterizations for birth-death chains and stability results to characterize essential self-adjointness for star-like graphs, and give some connections to the -Liouville property.
Keywords
Cite
@article{arxiv.2404.12531,
title = {Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity},
author = {Atsushi Inoue and Sean Ku and Jun Masamune and Radosław K. Wojciechowski},
journal= {arXiv preprint arXiv:2404.12531},
year = {2024}
}