Publisher DOI: 10.1007/s00020-017-2388-4
Title: Absolutely Continuous Spectrum for Laplacians on Radial Metric Trees and Periodicity
Language: English
Authors: Rohleder, Jonathan 
Seifert, Christian  
Keywords: Absolutely continuous spectrum; Quantum graph; Schrödinger operator; Tree
Issue Date: 1-Nov-2017
Source: Integral Equations and Operator Theory 3 (89): 439-453 (2017-11-01)
Abstract (english): 
On an infinite, radial metric tree graph we consider the corresponding Laplacian equipped with self-adjoint vertex conditions from a large class including δ- and weighted δ′-couplings. Assuming the numbers of different edge lengths, branching numbers and different coupling conditions to be finite, we prove that the presence of absolutely continuous spectrum implies that the sequence of geometric data of the tree as well as the coupling conditions are eventually periodic. On the other hand, we provide examples of self-adjoint, non-periodic couplings which admit absolutely continuous spectrum.
URI: http://hdl.handle.net/11420/3824
ISSN: 0378-620X
Journal: Integral equations and operator theory 
Institute: Mathematik E-10 
Document Type: Article
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