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Published August 2009 | Submitted
Journal Article Open

Singular spectrum for radial trees

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.

Additional Information

© 2009 World Scientific. Received 25 March 2009; Revised 10 July 2009. We are grateful to Barry Simon for useful discussions. RF appreciates the warm hospitality of Caltech, where part of this work has been done, and acknowledges support through DAAD grant D/06/49117.

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