The Gauß-Bonnet operator of an infinite graph
arXiv:1301.0739
Abstract
We propose a general condition, to ensure essential self-adjointness for the Gauß-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.
will appear in : Analysis and Mathematical Physics. DOI: 10.1007/s13324-014-0090-0