Essential self-adjointness of discrete magnetic Schrödinger operators

Details Essential self-adjointness of discrete magnetic Schrödinger operators Essential self-adjointness of discrete magnetic Schrödinger operators

2011-05-16

arxiv.org/abs/1105.3129v1

Mathematics

Spectral Theory

16 pages

Scientific paper

In the context of a locally finite weighted graph with vertex set $V$, we give a sufficient condition for the essential self-adjointness of the operator $\Delta_{\sigma}+W$, where $\Delta_{\sigma}$ is the magnetic Laplacian and $W\colon V\to\mathbb{R}$ is a function satisfying $W(x)\geq -q(x)$ for all $x\in V$, with $q\colon V\to [1,\infty)$. 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.

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