I. Netuka

activity

20062020

collaborators

Showing math.APShow all

6 papers · 1 filter

math.AP2020

On Evans' and Choquet's theorems on polar sets

Wolfhard Hansen, Ivan Netuka

By classical results of G.C. Evans and G. Choquet on "good kernels $G$ in potential theory", for every polar $K_{σ}$ -set $P$ , there exists a finite measure $μ$ on $P$ such that $Gμ=\…

math.AP2017

Semipolar sets and intrinsic Hausdorff measure

Wolfhard Hansen, Ivan Netuka

Given a "Green function" $G$ on a locally compact space $X$ with countable base, a Borel set $A$ in $X$ is called $G$ -semipolar, if there is no measure $ν \neq = 0$ supported by $A$ su…

math.AP2017

Nearly hyperharmonic functions and Jensen measures

Wolfhard Hansen, Ivan Netuka

Let $(X, H)$ be a $P$ -harmonic space and assume for simplicity that constants are harmonic. Given a numerical function $φ$ on $X$ which is locally lower bounded, l…

math.AP2016

Scaling invariant Harnack inequalities in a general setting

Wolfhard Hansen, Ivan Netuka

In a setting, where only "exit measures" are given, as they are associated with an arbitrary right continuous strong Markov process on a separable metric space, we provide simple c…

math.AP2012

Champagne subdomains with unavoidable bubbles

Wolfhard Hansen, Ivan Netuka

A champagne subdomain of a connected open set $U \neq = \emptyset$ in $R^{d}$ , $d \geq 2$ , is obtained omitting pairwise disjoint closed balls $B ˉ (x, r_{x})$ , $x \in X$ , the bubbles, where…

math.AP2006

Convexity of limits of harmonic measures

Wolfhard Hansen, Ivan Netuka

It is shown that, given a point $x\in\mathbbm{R}^d$, $d \geq 2$ , and open sets $U_{1}, ..., U_{k}$ containing $x$ , any convex combination of the harmonic measures for $x$ with respect to $…