English

Singular spectrum for radial trees

Spectral Theory 2015-05-13 v1 Mathematical Physics math.MP

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.

Cite

@article{arxiv.0806.0649,
  title  = {Singular spectrum for radial trees},
  author = {Jonathan Breuer and Rupert L. Frank},
  journal= {arXiv preprint arXiv:0806.0649},
  year   = {2015}
}

Comments

15 pages

R2 v1 2026-06-21T10:47:13.503Z