The Fekete-Szegő theorem with splitting conditions: Part II
The finite integral transform method for a parabolic differential equation on a graph.
The form boundedness criterion for the relativistic Schrödinger operator
We establish necessary and sufficient conditions on the real- or complex-valued potential defined on for the relativistic Schrödinger operator to be bounded as an operator from the Sobolev space to its dual .
The Functional Equation
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 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 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.