离散磁薛定谔算子的Sears型自伴性结果
A Sears-type self-adjointness result for discrete magnetic Schrödinger operators
摘要：
在顶点集为$V$且顶点度有界的赋权图的背景下，给出了算子$Δ_σ+W$的本质自伴性的一个充分条件，其中$Δ_σ$是磁拉普拉斯算子，$W\colon V\to\mathbb{R}$是对所有$x\in V$满足$W(x)\geq -q(x)$的函数，且有$q\colon V\to [1,\infty)$ .该条件表示在依赖于$q$和图的权重的度量的完整性方面。主要结果是I. Oleinik和M. A. Shubin在非紧黎曼流形的背景下。
英文摘要：
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 $W\colon V\to\mathbb{R}$ 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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