A Probabilistic Proof and Applications of Wiener's Test for the Heat Operator.
A uniform boundary Harnack inequality on non-tangentially accessible domains.
Asymptotics for some Green Kernels on the Heisenberg Group and the Martin Boundary.
Biharmonic morphisms
Let and be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from to is a continuous map from to which preserves the biharmonic structures of and . In the present work we study this notion and characterize in some cases the biharmonic morphisms between and in terms of harmonic morphisms between the harmonic spaces associated with and and the coupling kernels of them.
Boundary behaviour of eigenfunctions of the Laplacian in a bi-tree.
Comportement asymptotique des fonctions harmoniques sur les arbres
Comportement harmonique des densités conformes et frontière de Martin
Traitant la série de Poincaré d’un groupe discret d’isométries en courbure négative comme un noyau de Green, on établit une théorie du potentiel assez comparable à la théorie classique pour affirmer un parallèle entre densités conformes à la Patterson-Sullivan et densités harmoniques, et notamment définir une frontière de Martin où les densités ergodiques forment la partie minimale, et enfin l’identifier géométriquement sous hypothèse d’hyperbolicité.
Dirchlet's problem on Green lines and some convergence theorems for Denjoy's domains.
Doubling conditions for harmonic measure in John domains
We introduce new classes of domains, i.e., semi-uniform domains and inner semi-uniform domains. Both of them are intermediate between the class of John domains and the class of uniform domains. Under the capacity density condition, we show that the harmonic measure of a John domain satisfies certain doubling conditions if and only if is a semi-uniform domain or an inner semi-uniform domain.
Extreme Nonmonotoneity of the Picard Principle.
Fatou and Littlewood related theorems and a convergence property in the R.S. Martin topology.
Green functions for killed random walks in the Weyl chamber of Sp(4)
We consider a family of random walks killed at the boundary of the Weyl chamber of the dual of Sp(4), which in addition satisfies the following property: for any n ≥ 3, there is in this family a walk associated with a reflection group of order 2n. Moreover, the case n = 4 corresponds to a process which appears naturally by studying quantum random walks on the dual of Sp(4). For all the processes belonging to this family, we find the exact asymptotic of the Green functions along all infinite paths...
Harmonic majorization of in subsets of , .
Local Fatou theorem and the density of energy on manifolds of negative curvature.
Martin boundary associated with a system of PDE
In this paper, we study the Martin boundary associated with a harmonic structure given by a coupled partial differential equations system. We give an integral representation for non negative harmonic functions of this structure. In particular, we obtain such results for biharmonic functions (i.e. ) and for non negative solutions of the equation .
Martin boundary for homogeneous riemannian manifolds of negative curvature at the bottom of the spectrum.
In this paper we treat noncoercive operators on simply connected homogeneous manifolds of negative curvature.
Martin boundary for Schrödinger operators with singularity.
Martin boundary theory of some quantum random walks
Martin compactification and asymptotics of Green functions for Schrödinger operators with anisotropic potentials.
Mean values and harmonic functions.