Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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

Abstract : 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.
Complete list of metadatas

Cited literature [34 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02519206
Contributor : Sylvain Golenia <>
Submitted on : Wednesday, March 25, 2020 - 6:33:59 PM
Last modification on : Wednesday, July 15, 2020 - 9:22:01 AM
Document(s) archivé(s) le : Friday, June 26, 2020 - 3:23:03 PM

Files

klaussparse v6d.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02519206, version 1
  • ARXIV : 2003.11792

Collections

Citation

Sylvain Golenia, Françoise Truc. THE ESSENTIAL SPECTRUM OF THE DISCRETE LAPLACIAN ON KLAUS-SPARSE GRAPHS. 2020. ⟨hal-02519206⟩

Share

Metrics

Record views

34

Files downloads

22