BONNEFONT, Michel; JOULIN, Aldéric

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BONNEFONT, Michel
Institut de Mathématiques de Bordeaux [IMB]

JOULIN, Aldéric
Institut de Mathématiques de Toulouse UMR5219 [IMT]

Langue

Document de travail - Pré-publication

Résumé en anglais

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.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192866

Project ANR

Analyse Réelle et Géométrie - ANR-18-CE40-0012
Méthode de Stein et Analyse - ANR-18-CE40-0006

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251