The paper deals with the theory of inner (outer) capacities on locally compact spaces with
respect to general function kernels, the main emphasis being placed on the establishment of …

The paper deals with minimum energy problems in the presence of external fields on a
locally compact space X with respect to a function kernel κ satisfying the energy and …

In this paper, we investigate Riesz energy problems on unbounded conductors in R d in the
presence of general external fields Q, not necessarily satisfying the growth condition Q …

The paper deals with the theory of potentials with respect to the α-Riesz kernel| x− y| α− n of
order α∈(0, 2] on ℝ n, n≥ 3. Focusing first on the inner α-harmonic measure ε y A (ε y being …

For the Riesz kernel κ α (x, y):=| xy| α-n of order 0< α< n on R n, n⩾ 2, we introduce the so-
called inner pseudo-balayage ω^ A of a (Radon) measure ω on R n to a set A⊂ R n as the …

We describe a framework for extending the asymptotic behavior of a short-range interaction
from the unit cube to general compact subsets of $\mathbb R^ d $. This framework allows us …

In,, we study the constructive and numerical solution of minimizing the energy relative to the
Riesz kernel, where, for the Gauss variational problem, considered for finitely many …

We continue our investigation of the Gauss variational problem for infinite dimensional
vector measures on a locally compact space, associated with a condenser (A i) i∈ I. It has …

In Rn, n⩾ 2, we study the constructive and numerical solution of minimizing the energy
relative to the Riesz kernel| x− y| α− n, where 1< α< n, for the Gauss variational problem …

We study the constrained minimum energy problem with an external field relative to the α-
Riesz kernel x− y α− n of order α∈(0, n) for a generalized condenser A=(A i) i∈ I in ℝ n, n⩾ …