Effective perturbation theory for linear operators - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Journal of Operator Theory Année : 2019

Effective perturbation theory for linear operators

Résumé

We propose a new approach to the spectral theory of perturbed linear operators , in the case of a simple isolated eigenvalue. We obtain two kind of results: "radius bounds" which ensure perturbation theory applies for perturbations up to an explicit size, and "regularity bounds" which control the variations of eigendata to any order. Our method is based on the Implicit Function Theorem and proceeds by establishing differential inequalities on two natural quantities: the norm of the projection to the eigendirection, and the norm of the reduced resolvent. We obtain completely explicit results without any assumption on the underlying Banach space. In companion articles, on the one hand we apply the regularity bounds to Markov chains, obtaining non-asymptotic concentration and Berry-Esséen inequalities with explicit constants, and on the other hand we apply the radius bounds to transfer operator of intermittent maps, obtaining explicit high-temperature regimes where a spectral gap occurs.
Fichier principal
Vignette du fichier
perturbation.pdf (236.55 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01496106 , version 1 (27-03-2017)
hal-01496106 , version 2 (28-05-2020)

Identifiants

Citer

Benoît Kloeckner. Effective perturbation theory for linear operators. Journal of Operator Theory, 2019. ⟨hal-01496106v2⟩
101 Consultations
977 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More