论文标题
图在图上的本征函数和R-limits的生长
Growth of Eigenfunctions and R-limits on Graphs
论文作者
论文摘要
Schrödingeroperators of Infinite图的必需频谱$σ_{\ text Ess} $的表征涉及$ \ Mathcal {r} $限制的概念。这个概念是在$ \ mathbb {n} $和$ \ mathbb {z}^d $作为“ Right-limits”上介绍的$ \ mathbb {n} $上引入的概念，可捕获无限属性操作员的行为。对于具有子指数增长率的图表，我们显示$σ_ {\ text ess}（h）$中的每个点对应于相应的$ \ MATHCAL {r} $限制的有限的广义特征函数 - $ h $。如果此外，该图是均匀的亚指数生长，则相反的包容性也可以。
A characterization of the essential spectrum $σ_{\text ess}$ of Schrödinger operators on infinite graphs is derived involving the concept of $\mathcal{R}$-limits. This concept, which was introduced previously for operators on $\mathbb{N}$ and $\mathbb{Z}^d$ as "right-limits", captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate we show that each point in $σ_{\text ess}(H)$ corresponds to a bounded generalized eigenfunction of a corresponding $\mathcal{R}$-limit of $H$. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.
