The Gauss-Bonnet operator of an infinite graph. (English) Zbl 1323.05095
Summary: We propose a general condition, to ensure essential self-adjointness for the Gauss-Bonnet operator \(D=d+\delta\), based on a notion of completeness of Chernoff. This gives essential self-adjointness of the Laplace operator both for functions and 1-forms on infinite graphs. This is used to extend Flanders result concerning solutions of Kirchhoff’s laws.
MSC:
| 05C63 | Infinite graphs |
| 05C12 | Distance in graphs |
| 05C50 | Graphs and linear algebra (matrices, eigenvalues, etc.) |
| 39A12 | Discrete version of topics in analysis |
| 47B25 | Linear symmetric and selfadjoint operators (unbounded) |
Keywords:
infinite graph; \(\chi\)-completeness; difference operator; coboundary operator; Dirac type operator; Gauss-Bonnet operator; essential self-adjointnessReferences:
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