A Sears-type self-adjointness result for discrete magnetic Schrödinger operators
In the context of a weighted graph with vertex set V and bounded vertex degree, we give a sufficient condition for the essential self-adjointness of the operator δ σ+W, where δ σ is the magnetic Laplacian and W:V→R is a function satisfying W(x)≥-q(x) for all x∈V, with q:V→[1, ∞). The condition is expressed in terms of completeness of a metric that depends on q and the weights of the graph. The main result is a discrete analogue of the results of I. Oleinik and M.A. Shubin in the setting of non-compact Riemannian manifolds. © 2012 Elsevier Ltd.
Journal of Mathematical Analysis and Applications
Digital Object Identifier (DOI)
Milatovic. (2012). A Sears-type self-adjointness result for discrete magnetic Schrödinger operators. Journal of Mathematical Analysis and Applications, 396(2), 801–809. https://doi.org/10.1016/j.jmaa.2012.07.028