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Intertwining relations for one-dimensional diffusions and application to functional inequalities

Abstract : Following the recent work [13] fulfilled in the discrete case, we pro- vide in this paper new intertwining relations for semigroups of one-dimensional diffusions. Various applications of these results are investigated, among them the famous variational formula of the spectral gap derived by Chen and Wang [15] together with a new criterion ensuring that the logarithmic Sobolev inequality holds. We complete this work by revisiting some classical examples, for which new estimates on the optimal constants are derived.
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Submitted on : Friday, April 12, 2013 - 9:04:29 AM
Last modification on : Wednesday, June 9, 2021 - 10:00:07 AM
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Michel Bonnefont, Aldéric Joulin. Intertwining relations for one-dimensional diffusions and application to functional inequalities. Potential Analysis, Springer Verlag, 2014, 41, ⟨10.1007/s11118-014-9408-7⟩. ⟨hal-00812346⟩

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