Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees

Details Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees

2006-04-26

arxiv.org/abs/math/0604552v1

Mathematics

Spectral Theory

Scientific paper

10.1007/s00220-006-0121-2

We present examples of rooted tree graphs for which the Laplacian has singular continuous spectral measures. For some of these examples we further establish fractional Hausdorff dimensions. The singular continuous components, in these models, have an interesting multiplicity structure. The results are obtained via a decomposition of the Laplacian into a direct sum of Jacobi matrices.

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