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

Michel Bonnefont; Aldéric Joulin

doi:10.1007/s11118-014-9408-7

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arXiv · 1304.3595

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

Michel Bonnefont·Aldéric Joulin

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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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BibTeX RIS

Michel Bonnefont, Aldéric Joulin. 2013-04-12. Intertwining relations for one-dimensional diffusions and application to functional inequalities. https://doi.org/10.1007/s11118-014-9408-7

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