Point Spectrum of Periodic Operators on Universal Covering Trees

Abstract For any multi-graph $G$ with edge weights and vertex potential, its universal covering tree ${\mathcal{T}}$, we completely characterize the point spectrum of operators $A_{{\mathcal{T}}}$ on ${\mathcal{T}}$ arising as pull-backs local, self-adjoint $A_{G}$ $G$. This builds work Aomoto, includes an alternative proof necessary condition for derived in [ 5]. Our result gives a finite time algorithm to compute from graph $G$, additionally allows us show that this is itself contained $A_{G}$. Finally, prove typical pull-back have spectral delocalization property: set weight potential parameters giving rise purely absolutely continuous open, complement has large codimension.