15 research outputs found
Essential self-adjointness for combinatorial Schr\"odinger operators II- Metrically non complete graphs
We consider weighted graphs, we equip them with a metric structure given by a
weighted distance, and we discuss essential self-adjointness for weighted graph
Laplacians and Schr\"odinger operators in the metrically non complete case.Comment: Revisited version: Ognjen Milatovic wrote to us that he had
discovered a gap in the proof of theorem 4.2 of our paper. As a consequence
we propose to make an additional assumption (regularity property of the
graph) to this theorem. A new subsection (4.1) is devoted to the study of
this property and some details have been changed in the proof of theorem 4.
Intertwining relations for one-dimensional diffusions and application to functional inequalities
International audienceFollowing 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
Linear and nonlinear ultraparabolic equations of Kolmogorov type arising in diffusion theory and in finance
This paper contains a survey on a series of papers by the authors, dealing with linear and non linear Kolmogorov-type operators, arising in diffusion theory, probability and finance. Some new results, about existence for Cauchy problems, regularity propertiesand pointwise estimates of solutions, are also announced