Abstract
In this paper, we use the Nelson lemma to give a new proof for the essential self-adjointness of the discrete Laplace operator acting on 3-cochains, which we are defined in our previous paper [A. Baalal and K. Hatim, The discrete Laplacian of a 3-simplicial complex (2019), https://hal.archives-ouvertes.fr/hal-02105789 ]. Moreover, we establish on the infimum of the essential spectrum an upper bound.
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