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Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees

Pavel Exner Christian Seifert Peter Stollmann

TBD mathscidoc:1910.43220

Annales Henri Poincar, 15, (6), 1109-1121, 2014.6
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):929945, 2009) in the discrete case as well as for sparse trees in the metric case.
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@inproceedings{pavel2014absence,
  title={Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees},
  author={Pavel Exner, Christian Seifert, and Peter Stollmann},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133723488143749},
  booktitle={Annales Henri Poincar},
  volume={15},
  number={6},
  pages={1109-1121},
  year={2014},
}
Pavel Exner, Christian Seifert, and Peter Stollmann. Absence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial trees. 2014. Vol. 15. In Annales Henri Poincar. pp.1109-1121. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020133723488143749.
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