Annales Henri Poincaré

, Volume 15, Issue 6, pp 1109–1121 | Cite as

Absence of Absolutely Continuous Spectrum for the Kirchhoff Laplacian on Radial Trees

Article

Abstract

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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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Pavel Exner
    • 1
    • 2
  • Christian Seifert
    • 3
  • Peter Stollmann
    • 4
  1. 1.Doppler Institute for Mathematical Physics and Applied Mathematics, Faculty of Nuclear Sciences and Physical EngineeringCzech Technical UniversityPragueCzech Republic
  2. 2.Nuclear Physics Institute ASCRŘež near PragueCzech Republic
  3. 3.Institut für MathematikTechnische Universität Hamburg-HarburgHamburgGermany
  4. 4.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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