A note on eigenvalues estimates for one-dimensional diffusion operators - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

A note on eigenvalues estimates for one-dimensional diffusion operators

Michel Bonnefont

Résumé

Dealing with one-dimensional diffusion operators, we obtain upper and lower variational formulae on the eigenvalues given by the max-min principle, generalizing the celebrated result of Chen and Wang on the spectral gap. Our inequalities reveal to be sharp at least when the eigenvalues considered belong to the discrete spectrum of the operator, since in this case both lower and upper bounds coincide and involve the associated eigenfunctions. Based on the intertwinings between diffusion operators and some convenient gradients with weights, our approach also allows to estimate the gap between the two first positive eigenvalues when the spectral gap belongs to the discrete spectrum.
Fichier principal
Vignette du fichier
BJ_final.pdf (285.44 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02138739 , version 1 (24-05-2019)

Identifiants

Citer

Michel Bonnefont, Aldéric Joulin. A note on eigenvalues estimates for one-dimensional diffusion operators. 2019. ⟨hal-02138739⟩
59 Consultations
106 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More