Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees
نویسندگان
چکیده
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 [3] in the discrete case as well as for sparse trees in the metric case. MSC2010: 34L05, 34L40, 35Q40
منابع مشابه
Singular Spectrum for Radial Trees
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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