|Publisher DOI:||10.1007/s00023-013-0274-4||Title:||Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees||Language:||English||Authors:||Exner, Pavel
|Issue Date:||12-Jul-2013||Publisher:||Springer International Publishing AG||Source:||Annales Henri Poincare 15 (6): 1109-1121 (2014)||Abstract (english):||
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. © 2013 Springer Basel.
|URI:||http://hdl.handle.net/11420/9949||ISSN:||1424-0661||Institute:||Mathematik E-10||Document Type:||Article||Journal:||Annales Henri Poincaré|
|Appears in Collections:||Publications without fulltext|
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