The adjacency matrix and the discrete Laplacian acting on forms

Published 22 May 2015 in math.SP and math.FA | (1505.06109v1)

Abstract: We study the relationship between the adjacency matrix and the discrete Laplacian acting on 1-forms. We also prove that if the adjacency matrix is bounded from below it is not necessarily essentially self-adjoint. We discuss the question of essential self-adjointness and the notion of completeness.

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