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 
Seifert, Christian  
Stollmann, Peter 
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 
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