-uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients
La théorie des espaces fonctionnels à nullité 1 et le problème de Neumann sur les espaces harmoniques
On introduit les espaces fonctionnels dans lesquels l’opérateur potentiel satisfait au principe semi-complet du maximum si et seulement si la contraction module opère. Un tel espace fonctionnel sur la frontière de Martin d’un espace harmonique symétrique de Brelot est envisagé à l’aide du noyau de Naïm. Il est isomorphe à l’espace de Dirichlet des fonctions harmoniques. L’opérateur potentiel de cet espace donne la solution du problème de Neumann. On introduit l’espace de Dirichlet des fonctions...
Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group
Liouville theorems based on symmetric diffusions
Local property of Dirichlet forms and diffusions on general state spaces.
(Nonsymmetric) Dirichlet operators on : existence, uniqueness and associated Markov processes
Non-Symmetric Translation Invariant Dirichlet Forms.
On a construction of Markov processes associated with time dependent Dirichlet spaces.
On a theorem of Cartan
On absorption times and Dirichlet eigenvalues
This paper gives a stochastic representation in spectral terms for the absorption time T of a finite Markov chain which is irreducible and reversible outside the absorbing point. This yields quantitative informations on the parameters of a similar representation due to O'Cinneide for general chains admitting real eigenvalues. In the discrete time setting, if the underlying Dirichlet eigenvalues (namely the eigenvalues of the Markov transition operator restricted to the functions vanishing on...
On an extension of jump-type symmetric Dirichlet forms.
On Lebesgue points of functions in the Sobolev class .
On (r, 2)-capacities for a class of elliptic pseudo differential operators.
On semi-martingale characterizations of functionals of symmetric Markov processes.
On the relation between elliptic and parabolic Harnack inequalities
We show that, if a certain Sobolev inequality holds, then a scale-invariant elliptic Harnack inequality suffices to imply its a priori stronger parabolic counterpart. Neither the relative Sobolev inequality nor the elliptic Harnack inequality alone suffices to imply the parabolic Harnack inequality in question; both are necessary conditions. As an application, we show the equivalence between parabolic Harnack inequality for on , (i.e., for ) and elliptic Harnack inequality for on .
On the representation of Dirichlet forms
A general representation theorem is obtained for positive quadratic forms, defined on (the space of continuously differentiable functions with compact support contained in ) which are local and on which all normal contractions operate.
On the Skew Product of Symmetric Diffusion Processes.
On the structure of subordinate semigroups.
Opérateurs carré du champ
Perturbation by differences of unbounded potentials.