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THE ESSENTIAL SPECTRUM OF THE DISCRETE LAPLACIAN ON KLAUS-SPARSE GRAPHS

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorGOLENIA, Sylvain
hal.structure.identifierInstitut Fourier [IF]
dc.contributor.authorTRUC, Françoise
dc.date.accessioned2024-04-04T02:55:09Z
dc.date.available2024-04-04T02:55:09Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192337
dc.description.abstractEnIn 1983, Klaus studied a class of potentials with bumps and computed the essential spectrum of the associated Schrödinger operator with the help of some localisations at infinity. A key hypothesis is that the distance between two consecutive bumps tends to infinity at infinity. In this article, we introduce a new class of graphs (with patterns) that mimics this situation, in the sense that the distance between two patterns tends to infinity at infinity. These patterns tend, in some way, to asymptotic graphs. They are the localisations at infinity. Our result is that the essential spectrum of the Laplacian acting on our graph is given by the union of the spectra of the Laplacian acting on the asymptotic graphs. We also discuss the question of the stability of the essential spectrum in the appendix.
dc.language.isoen
dc.title.enTHE ESSENTIAL SPECTRUM OF THE DISCRETE LAPLACIAN ON KLAUS-SPARSE GRAPHS
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halMathématiques [math]/Théorie spectrale [math.SP]
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.identifier.arxiv2003.11792
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-02519206
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02519206v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=GOLENIA,%20Sylvain&TRUC,%20Fran%C3%A7oise&rft.genre=preprint


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