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

Jonathan Breuer

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arXiv · math/0608159

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

Jonathan Breuer

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Abstract

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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BibTeX RIS

Jonathan Breuer. 2006-08-07. Singular Continuous and Dense Point Spectrum for Sparse Trees with Finite Dimensions. https://arxiv.org/abs/math/0608159

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