A note on eigenvalues estimates for one-dimensional diffusion operators
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | BONNEFONT, Michel | |
hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
dc.contributor.author | JOULIN, Aldéric | |
dc.date.accessioned | 2024-04-04T03:01:02Z | |
dc.date.available | 2024-04-04T03:01:02Z | |
dc.date.created | 2019-05-24 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192866 | |
dc.description.abstractEn | 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. | |
dc.description.sponsorship | Analyse Réelle et Géométrie - ANR-18-CE40-0012 | |
dc.description.sponsorship | Méthode de Stein et Analyse - ANR-18-CE40-0006 | |
dc.language.iso | en | |
dc.title.en | A note on eigenvalues estimates for one-dimensional diffusion operators | |
dc.type | Document de travail - Pré-publication | |
dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
dc.identifier.arxiv | 1906.02496 | |
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-02138739 | |
hal.version | 1 | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-02138739v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BONNEFONT,%20Michel&JOULIN,%20Ald%C3%A9ric&rft.genre=preprint |
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