Pure point spectrum of the Laplacians on fractal graphs
On two-point self-similar fractal graphs the authors consider Laplacians which correspond to the adjacency matrix and the simple random walk. Roughly speaking, it is proven that if the graph has an infinite number of cycles and the length of these cycles approaches infinity, then the spectrum is pure point and all eigenvalues have infinite multiplicity. It is also shown that a countable set of orthonormal eigenfunctions with compact support is complete.
scientific article; zbMATH DE number 764032