The General Riesz Decomposition and the Specific Order of Excessive Functions.
The Generalized Ahlfors-Heins Theorem in Certain d-Dimensional Cones.
The gradient lemma
We show that if a decreasing sequence of subharmonic functions converges to a function in then the convergence is in .
The Green formula and HP Spaces on trees.
The Harmonie Space Associated with a "Reasonable" Standard Process.
The heat and adjoint heat potentials
The Hölder duality for harmonic functions
The homogeneous transfinite diameter of a compact subset of
Let K be a compact subset of . A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of is computed.
The image of a finely holomorphic map is pluripolar
We prove that the image of a finely holomorphic map on a fine domain in ℂ is a pluripolar subset of ℂⁿ. We also discuss the relationship between pluripolar hulls and finely holomorphic functions.
The insertion of sets and fine topologies
The insertion of regular sets in potential theory
The integral equation methods for the perturbed Helmholtz eigenvalue problems.
The Intersection of the Closures of Two Disjoint Strongly Pseudoconvex Domains.
The inverse problem for elliptic equations from Dirichlet to Neumann map in multiply connected 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 Lusin-Menchoff property of fine topologies
The Martin Boundary for Harmonic Functions on Groups of Automorphisms of a Homogeneous Tree.
The Martin compactification of a plane domain
We prove that the Martin compactification of a plane domain is homeomorphic to a subset of the two-dimensional sphere.
The Martin compactification of the Cartesian product of two hyperbolic spaces.