Essential self-adjointness of a weighted 3-simplicial complex Laplacians.

In this paper, we construct a weighted 3 -simplicial complex S w = (V , E , F , T , w V , w E , w F , w T) on a connected oriented locally finite graph (V , E) by the introduction of the notion of oriented tetrahedrons T , the notion of oriented triangular faces F , a weight on V , a weight on E , a weight on F and a weight on T. Next, we create the weighted Gauss–Bonnet operator of S w and we use it to construct the weighted Laplacian associated to V , the weighted Laplacian associated to E , the weighted Laplacian associated to F , the weighted Laplacian associated to T and the weighted Laplacian associated to S w . After that, we introduce the notion of the χ -completeness of S w and we give necessary conditions for S w to be χ -complete. Finally, we prove that the weighted Gauss–Bonnet operator and the weighted Laplacians are essentially self-adjoint based on the χ -completeness. [ABSTRACT FROM AUTHOR]