Absence of Absolutely Continuous Spectrum for the Kirchhoff Laplacian on Radial Trees
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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.
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- 1.Berkolaiko, G., Kuchment, P.: Introduction to Quantum Graphs. Providence, RI, American Mathematical Society (2013)Google Scholar
- 2.Bessaga, C., Pelczynski, A.: Selected topics in infinite-dimensional topology. Mathematical Monographs, vol. 58. Polish Scientific, Warsaw (1975)Google Scholar
- 11.Seifert, C.: Measure-perturbed one-dimensional Schrödinger operators—a continuum model for quasicrystals. Dissertation thesis, Chemnitz University of Technology (2012). URL: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-102766