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

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cris.virtual.author-gnd1030178798
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cris.virtual.author-orcid0000-0001-9182-8687
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cris.virtual.departmentMathematik E-10
cris.virtual.department#PLACEHOLDER_PARENT_METADATA_VALUE#
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cris.virtualsource.author-orcid13366db6-e0c6-48a1-8440-966a7ce842ac
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datacite.resourceTypeOtheren_US
datacite.resourceTypeGeneralOtheren_US
dc.contributor.authorExner, Pavel
dc.contributor.authorSeifert, Christian
dc.contributor.authorStollmann, Peter
dc.date.accessioned2021-07-23T07:22:01Z
dc.date.available2021-07-23T07:22:01Z
dc.date.issued2013-07-12
dc.description.abstractIn 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.en
dc.identifier.citationAnnales Henri Poincare 15 (6): 1109-1121 (2014)de_DE
dc.identifier.scopus2-s2.0-84901193662de_DE
dc.identifier.urihttp://hdl.handle.net/11420/9949
dc.language.isoende_DE
dc.publisherSpringer International Publishing AGde_DE
dc.relation.ispartofAnnales Henri Poincaréde_DE
dc.relation.issn1424-0661de_DE
dc.subject.ddc510: Mathematikde_DE
dc.titleAbsence of absolutely continuous spectrum for the Kirchhoff Laplacian on radial treesde_DE
dc.typeJournal Articlede_DE
dc.type.casraiOtheren_US
dc.type.diniOtheren_US
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dcterms.DCMITypeOtheren_US
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local.status.inpressfalsede_DE
local.type.legacyArticle
oaire.citation.endPage1121de_DE
oaire.citation.issue6de_DE
oaire.citation.startPage1109de_DE
oaire.citation.volume15de_DE
tuhh.abstract.englishIn 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.de_DE
tuhh.publication.instituteMathematik E-10de_DE
tuhh.publisher.doi10.1007/s00023-013-0274-4
tuhh.type.opusOtheren_US

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