# Absence of Absolutely Continuous Spectrum for the Kirchhoff Laplacian on Radial Trees

@article{Exner2014AbsenceOA, title={Absence of Absolutely Continuous Spectrum for the Kirchhoff Laplacian on Radial Trees}, author={P. Exner and C. Seifert and P. Stollmann}, journal={Annales Henri Poincar{\'e}}, year={2014}, volume={15}, pages={1109-1121} }

In this paper, we prove that the existence of absolutely continuous spectrum of the Kirchhoff Laplacian on a radial metric tree graph together with a finite complexity of the geometry of the tree implies that the tree is in fact eventually periodic. This complements the results by Breuer and Frank in (Rev Math Phys 21(7):929–945, 2009) in the discrete case as well as for sparse trees in the metric case.

4 Citations

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