THE ESSENTIAL SPECTRUM OF THE DISCRETE LAPLACIAN ON KLAUS-SPARSE GRAPHS
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | GOLENIA, Sylvain | |
| hal.structure.identifier | Institut Fourier [IF] | |
| dc.contributor.author | TRUC, Françoise | |
| dc.date.accessioned | 2024-04-04T02:55:09Z | |
| dc.date.available | 2024-04-04T02:55:09Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192337 | |
| dc.description.abstractEn | In 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.iso | en | |
| dc.title.en | THE ESSENTIAL SPECTRUM OF THE DISCRETE LAPLACIAN ON KLAUS-SPARSE GRAPHS | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.subject.hal | Mathématiques [math]/Théorie spectrale [math.SP] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.identifier.arxiv | 2003.11792 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-02519206 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02519206v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=GOLENIA,%20Sylvain&TRUC,%20Fran%C3%A7oise&rft.genre=preprint |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||