Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910415087206400 |
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| author | Inoue, Atsushi Ku, Sean Masamune, Jun Wojciechowski, Radosław K. |
| author_facet | Inoue, Atsushi Ku, Sean Masamune, Jun Wojciechowski, Radosław K. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12531 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity Inoue, Atsushi Ku, Sean Masamune, Jun Wojciechowski, Radosław K. Functional Analysis 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. |
| title | Essential self-adjointness of the Laplacian on weighted graphs: harmonic functions, stability, characterizations and capacity |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.12531 |