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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBONNEFONT, Michel
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorJOULIN, Aldéric
dc.date.accessioned2024-04-04T03:01:02Z
dc.date.available2024-04-04T03:01:02Z
dc.date.created2019-05-24
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192866
dc.description.abstractEnDealing 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.sponsorshipAnalyse Réelle et Géométrie - ANR-18-CE40-0012
dc.description.sponsorshipMéthode de Stein et Analyse - ANR-18-CE40-0006
dc.language.isoen
dc.title.enA note on eigenvalues estimates for one-dimensional diffusion operators
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Probabilités [math.PR]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.identifier.arxiv1906.02496
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-02138739
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02138739v1
bordeaux.COinSctx_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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