Singular Continuous and Dense Point Spectrum for Sparse Trees with Finite Dimensions

Details Singular Continuous and Dense Point Spectrum for Sparse Trees with Finite Dimensions Singular Continuous and Dense Point Spectrum for Sparse Trees with Finite Dimensions

2006-08-07

arxiv.org/abs/math/0608159v1

Mathematics

Spectral Theory

Scientific paper

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.

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