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.

References in corpus (3)

• Weighted Poincaré-type inequalities for Cauchy and other convex measures
• Intertwining and commutation relations for birth-death processes
• Improved spectral gap bounds on positively curved manifolds

Cited by in corpus (1)

• Fokker-Planck equations and one-dimensional functional inequalities for heavy tailed densities