Singular continuous spectrum for the Laplacian on certain sparse trees

Jonathan Breuer

doi:10.1007/s00220-006-0121-2

Singular continuous spectrum for the Laplacian on certain sparse trees

Jonathan Breuer^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	851-857
Number of pages	7
Journal	Communications in Mathematical Physics
Volume	269
Issue number	3
DOIs	https://doi.org/10.1007/s00220-006-0121-2
State	Published - Feb 2007

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abstract = "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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Singular continuous spectrum for the Laplacian on certain sparse trees

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