Singular spectrum for radial trees

Details Singular spectrum for radial trees Singular spectrum for radial trees

2008-06-03

arxiv.org/abs/0806.0649v1

Rev. Math. Phys. 21 (2009), no. 7, 1 - 17

Mathematics

Spectral Theory

15 pages

Scientific paper

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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