Spectral Theory of Infinite Quantum Graphs
dc.bibliographicCitation.firstPage | 3457 | |
dc.bibliographicCitation.issue | 11 | |
dc.bibliographicCitation.lastPage | 3510 | |
dc.bibliographicCitation.volume | 19 | |
dc.contributor.author | Exner, Pavel | |
dc.contributor.author | Kostenko, Aleksey | |
dc.contributor.author | Malamud, Mark | |
dc.contributor.author | Neidhardt, Hagen | |
dc.date.accessioned | 2023-02-06T10:22:45Z | |
dc.date.available | 2023-02-06T10:22:45Z | |
dc.date.issued | 2018 | |
dc.description.abstract | We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a close connection between spectral properties of a quantum graph and the corresponding properties of a certain weighted discrete Laplacian on the underlying discrete graph. Using this connection together with spectral theory of (unbounded) discrete Laplacians on infinite graphs, we prove a number of new results on spectral properties of quantum graphs. Namely, we prove several self-adjointness results including a Gaffney-type theorem. We investigate the problem of lower semiboundedness, prove several spectral estimates (bounds for the bottom of spectra and essential spectra of quantum graphs, CLR-type estimates) and study spectral types. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/11287 | |
dc.identifier.uri | http://dx.doi.org/10.34657/10323 | |
dc.language.iso | eng | |
dc.publisher | Cham (ZG) : Springer International Publishing AG | |
dc.relation.doi | https://doi.org/10.1007/s00023-018-0728-9 | |
dc.relation.essn | 1424-0661 | |
dc.relation.ispartofseries | Annales Henri Poincaré 19 (2018), Nr. 11 | eng |
dc.relation.issn | 1424-0637 | |
dc.rights.license | CC BY 4.0 Unported | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0 | |
dc.subject | self-adjoint extensions | eng |
dc.subject | dimensional schrodinger operator | eng |
dc.subject | boundary-value-problems | eng |
dc.subject | dirichlet forms | eng |
dc.subject | laplacian | eng |
dc.subject | approximation | eng |
dc.subject | convergence | eng |
dc.subject | couplings | eng |
dc.subject | networks | eng |
dc.subject | matrices | eng |
dc.subject.ddc | 530 | |
dc.subject.ddc | 510 | |
dc.title | Spectral Theory of Infinite Quantum Graphs | eng |
dc.type | article | |
dc.type | Text | |
dcterms.bibliographicCitation.journalTitle | Annales Henri Poincaré | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Physik | ger |
wgl.subject | Mathematik | ger |
wgl.type | Zeitschriftenartikel | ger |
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