The insertion of sets and fine topologies
The Intersection of the Closures of Two Disjoint Strongly Pseudoconvex Domains.
The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces
We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.
The logarithmic capacity in
The Martin Boundary for Harmonic Functions on Groups of Automorphisms of a Homogeneous Tree.
The Martin compactification of the Cartesian product of two hyperbolic spaces.
The Martin compactification of the polydisc at the bottom of the positive spectrum.
The Max-Plus Martin boundary.
The Partial Legendre Transformation for Plurisubharmonic Functions.
The Pluripolar Hull and the Fine Topology
We show that the projections of the pluripolar hull of the graph of an analytic function in a subdomain of the complex plane are open in the fine topology.
The Poisson boundary for rank one manifolds and their compact lattices.
The Poisson Boundary of the Mapping Class Group and of Teichmüller Space
The Poisson formula for groups with hyperbolic properties.
The Poisson integral for a ball in spaces of constant curvature
We present explicit expressions of the Poisson kernels for geodesic balls in the higher dimensional spheres and real hyperbolic spaces. As a consequence, the Dirichlet problem for the projective space is explicitly solved. Comparison of different expressions for the same Poisson kernel lead to interesting identities concerning special functions.
The Poisson Space of the Koranyi Ball.
The Poisson summation formula for a Dirichlet problem with gliding and glancing rays
The resolvent for a convolution kernel satisfying the domination principle
The restriction theorem for fully nonlinear subequations
Let be a submanifold of a manifold . We address the question: When do viscosity subsolutions of a fully nonlinear PDE on , restrict to be viscosity subsolutions of the restricted subequation on ? This is not always true, and conditions are required. We first prove a basic result which, in theory, can be applied to any subequation. Then two definitive results are obtained. The first applies to any “geometrically defined” subequation, and the second to any subequation which can be transformed...
The Schur harmonic convexity of the Hamy symmetric function and its applications.
The surjectivity of a constant coefficient homogeneous differential operator in the real analytic functions and the geometry of its symbol
Hörmander has characterized the surjective constant coefficient partial differential operators on the space of all real analytic functions on by a Phragmén-Lindelöf condition. Geometric implications of this condition and, for homogeneous operators, of the corresponding condition for Gevrey classes are given.