A general Choquet–Deny theorem for nilpotent groups
A generalization of the Phragmén-Lindelöf principle for elliptic differential equations.
A generalized Nevanlinna theorem for supertemperatures.
A Hilbert Lemniscate Theorem in
For a regular, compact, polynomially convex circled set in , we construct a sequence of pairs of homogeneous polynomials in two variables with
A non-linear Riesz respresentation in probabilistic potential theory
A Phragmén-Lindelöf Type Theorem for a Certain Class of Generalized Subharmonic Functions.
A strong Liouville theorem for -harmonic functions on graphs.
A Tauberian Theorem and Tangential Convergence for Bounded Harmonic Functions on Balls in ...n.
An example concerning the topological character of the zero-set of a harmonic function.
An infinite-harmonic analogue of a Lelong theorem and infinite-harmonicity cells.
Analytic discs method in complex analysis [Book]
Approach regions for trees and the unit disc.
Approximation et caractère de quasi-analyticité dans la théorie axiomatique des fonctions harmoniques
Dans le cadre de l’axiomatique de M. Brelot, et en utilisant la théorie des fonctions harmoniques adjointes de Madame R.M. Hervé, on caractérise la propriété de quasi-analycité notée : toute fonction harmonique adjointe dans un domaine est nulle dès qu’elle est nulle au voisinage d’un point. On montre que est équivalente à une propriété d’approximation de toute fonction réelle finie continue sur les frontières d’ouverts relativement compacts. Cette approximation est réalisée à l’aide de différences...
Asymptotic Behavior of Fundamental Solutions and Potential Theory of Prabolic Operators with Variable Coeeficients.
Asymptotic behaviour of generalized Poisson integrals in rank one symmetric spaces and in trees
Asymptotic paths for subsolutions of quasilinear elliptic equations.
Asymptotics for some Green Kernels on the Heisenberg Group and the Martin Boundary.
Boundary Harnack principle for separated semihyperbolic repellers, harmonic measure applications.
Boundary potential theory for stable Lévy processes
We investigate properties of harmonic functions of the symmetric stable Lévy process on without the assumption that the process is rotation invariant. Our main goal is to prove the boundary Harnack principle for Lipschitz domains. To this end we improve the estimates for the Poisson kernel obtained in a previous work. We also investigate properties of harmonic functions of Feynman-Kac semigroups based on the stable process. In particular, we prove the continuity and the Harnack inequality for...
Characterizations of p-superharmonic functions on metric spaces
We show the equivalence of some different definitions of p-superharmonic functions given in the literature. We also provide several other characterizations of p-superharmonicity. This is done in complete metric spaces equipped with a doubling measure and supporting a Poincaré inequality. There are many examples of such spaces. A new one given here is the union of a line (with the one-dimensional Lebesgue measure) and a triangle (with a two-dimensional weighted Lebesgue measure). Our results also...