Singular Continuous and Dense Point Spectrum for Sparse Trees with Finite Dimensions
谱理论
2007-05-23 v1 数学物理
math.MP
摘要
Sparse trees are trees with sparse branchings. The Laplacian on some of these trees can be shown to have singular spectral measures. We focus on a simple family of sparse trees for which the dimensions can be naturally defined and shown to be finite. Generically, this family has singular spectral measures and eigenvalues that are dense in some interval.
引用
@article{arxiv.math/0608159,
title = {Singular Continuous and Dense Point Spectrum for Sparse Trees with Finite Dimensions},
author = {Jonathan Breuer},
journal= {arXiv preprint arXiv:math/0608159},
year = {2007}
}