论文标题
通用树木上的定期操作员的点频谱
Point Spectrum of Periodic Operators on Universal Covering Trees
论文作者
论文摘要
对于任何具有边缘重量和顶点潜力的多段$ g $，以及其通用的树$ \ Mathcal {t} $，我们完全表征运算符$ a _ {\ Mathcal {t Mathcal {t}} $的点频谱，$ \ Mathcal {t} $ in Mathcal {t} $ a in proult-backss of local，$ a_________ $ a_ $ a_ $ a_ $ a_______这是基于AOMOTO的工作，其中包括他在他衍生的点频谱所必需条件的替代证明（Aomoto，1991）。我们的结果给出了有限的时间算法来计算图$ g $的$ a _ {\ mathcal {t}} $的点频谱，此外允许我们证明此点频谱包含在$ a_ {g} $的频谱中。最后，我们证明，典型的撤回后背现操作员具有光谱脱位属性：$ a_ {g} $的边缘重量和顶点潜在参数，产生$ a _ {\ Mathcal {t}} $，纯粹是绝对连续的频谱，并且其补充具有很大的编码。
For any multi-graph $G$ with edge weights and vertex potential, and its universal covering tree $\mathcal{T}$, we completely characterize the point spectrum of operators $A_{\mathcal{T}}$ on $\mathcal{T}$ arising as pull-backs of local, self-adjoint operators $A_{G}$ on $G$. This builds on work of Aomoto, and includes an alternative proof of the necessary condition for point spectrum he derived in (Aomoto, 1991). Our result gives a finite time algorithm to compute the point spectrum of $A_{\mathcal{T}}$ from the graph $G$, and additionally allows us to show that this point spectrum is contained in the spectrum of $A_{G}$. Finally, we prove that typical pull-back operators have a spectral delocalization property: the set of edge weight and vertex potential parameters of $A_{G}$ giving rise to $A_{\mathcal{T}}$ with purely absolutely continuous spectrum is open and its complement has large codimension.
