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arXiv · 2404.12531

Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity

Atsushi Inoue·Sean Ku·Jun Masamune·Radosław K. Wojciechowski
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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 Schrödinger 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 $\ell^2$-Liouville property.

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Atsushi Inoue, Sean Ku, Jun Masamune, Radosław K. Wojciechowski. 2024-04-18. Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity. https://arxiv.org/abs/2404.12531

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