The Gau-Bonnet operator of an infinite graph
Abstract
We propose a general condition, to ensure essential self-adjointness for the Gau-Bonnet operator, based on a notion of completeness as Chernoff. This gives essential self-adjointness of the Laplace operator both for functions or 1-forms on infinite graphs. This is used to extend Flanders result concerning solutions of Kirchhoff's laws.
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