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arXiv · 0806.0649

Singular spectrum for radial trees

Jonathan Breuer·Rupert L. Frank
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Abstract

We prove several results showing that absolutely continuous spectrum for the Laplacian on radial trees is a rare event. In particular, we show that metric trees with unbounded edges have purely singular spectrum and that generically (in the sense of Baire) radial trees have purely singular continuous spectrum.

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Jonathan Breuer, Rupert L. Frank. 2008-06-03. Singular spectrum for radial trees. https://doi.org/10.1142/s0129055x09003773

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