The paper deals with minimum energy problems in the presence of external fields with
respect to the Riesz kernels| x− y| α− n, 0< α< n, on R n, n⩾ 2. For quite a general (not …

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 …

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 …

For suitable kernels on a locally compact space $ X $, we develop a theory of inner
balayage of quite general Radon measures $\omega $(not necessarily of finite energy) to …

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 …

In the theory of inner and outer balayage of positive Radon measures on a locally compact
space $ X $ to arbitrary $ A\subset X $ with respect to suitable, quite general function …

Under suitable requirements on a kernel on a locally compact space, we develop a theory of
inner (outer) balayage of quite general Radon measures $\omega $(not necessarily of finite …

For suitable function kernels κ on a locally compact space, we develop a theory of inner
pseudo-balayage ω ̂ A of signed (Radon) measures ω of finite energy onto a quasiclosed …

Let $\mu $ be a positive measure supported on a domain $\Omega $. We consider the
behavior of the balayage measure $\nu:=\mathrm {Bal}(\mu,\partial\Omega) $ near a point …