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 the theory of balayage of (signed) Radon measures μ of finite energy
on a locally compact space X with respect to a consistent kernel κ satisfying the domination …

First introduced by J. Deny, the classical principle of positivity of mass states that if κ α μ⩽ κ α
ν everywhere on R n, then μ (R n)⩽ ν (R n). Here μ, ν are positive Radon measures on R n …

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 …

We develop a theory of inner balayage of a positive Radon measure μ of finite energy on a
locally compact space X to arbitrary A⊂ X, thereby generalizing Cartan's theory of …

We consider a minimal energy problem with an external field over noncompact classes of
infinite dimensional vector measures (μ^i)_i∈I on a locally compact space. The components …

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 consider a constrained minimal energy problem with an external field over noncompact
classes of vector measures (μi) i∈ I of finite or infinite dimensions on a locally compact …