I. Netuka

activity

20062020

most citedUnavoidable sets and harmonic measures living on small sets

16 citations · 17 across the 7 of their papers we have counts for

collaborators

13 papers

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.PR2018

Nearly hyperharmonic functions are infima of excessive functions

Wolfhard Hansen, Ivan Netuka

Let $X$ be a Hunt process on a locally compact space $X$ such that the set $E_{X}$ of its Borel measurable excessive functions separates points, every…

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

Reduced functions and Jensen measures

Wolfhard Hansen, Ivan Netuka

Let $φ$ be a locally upper bounded Borel measurable function on a Greenian open set $Ω$ in $R^{d}$ and, for every $x \in Ω$ , let $v_{φ} (x)$ denote the infimum of the integrals of $φ$ wi…

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.AP2014

Hunt's hypothesis (H) and the triangle property of the Green function

Wolfhard Hansen, Ivan Netuka

Let $X$ be a locally compact abelian group with countable base and let $W$ be a convex cone of positive numerical functions on $X$ which is invariant under the group actio…

math.AP2014★ 1 cited

Harnack inequalities for Hunt processes with Green function

Wolfhard Hansen, Ivan Netuka

Let $(X, W)$ be a balayage space, $1 \in W$ , or - equivalently - let $W$ be the set of excessive functions of a Hunt process on a locally compact space $X$ …

math.AP2013★ 16 cited

Unavoidable sets and harmonic measures living on small sets

Wolfhard Hansen, Ivan Netuka

Given a connected open set $U \neq = \emptyset$ in $R^{d}$ , $d \geq 2$ , a relatively closed set $A$ in $U$ is called \emph{unavoidable in $U$ }, if Brownian motion, starting in $x\in U\setm…

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.AP2012

Champagne subregions with unavoidable bubbles

Wolfhard Hansen, Ivan Netuka

A champagne subregion 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.AP2010

Jensen measures in potential theory

Wolfhard Hansen, Ivan Netuka

It is shown that, for open sets in classical potential theory and - more generally - for elliptic harmonic spaces, the set of Jensen measures for a point is a simple union of close…

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 $…