B. Fuglede

activity

20102019

most citedConstrained minimum Riesz energy problems for a condenser with intersecting plates

2 citations · 5 across the 10 of their papers we have counts for

collaborators

14 papers

math.FA2019

The Fuglede Theorem and Some Intertwining Relations

Ikram Fatima Zohra Bensaid, Souheyb Dehimi, Bent Fuglede +1

In this paper, we show a new and classic version of the celebrated Fuglede Theorem in an unbounded setting. A related counterexample is equally presented. In the second strand of t…

math.CA2018

Various concepts of Riesz energy of measures and application to condensers with touching plates

Bent Fuglede, Natalia Zorii

We investigate minimum weak $α$ -Riesz energy problems with external fields in both the unconstrained and constrained settings for generalized condensers $(A_{1}, A_{2})$ such that the c…

math.CA2018

An alternative concept of Riesz energy of measures with application to generalized condensers

Bent Fuglede, Natalia Zorii

In view of a recent example of a positive Radon measure $μ$ on a domain $D \subset R^{n}$ , $n ⩾ 3$ , such that $μ$ is of finite energy $E_{g} (μ)$ relative to the $α$ -Green k…

math.CA2018

Constrained minimum Riesz and Green energy problems for vector measures associated with a generalized condenser

Bent Fuglede, Natalia Zorii

For a finite collection $A = (A_{i})_{i \in I}$ of locally closed sets in $R^{n}$ , $n ⩾ 3$ , with the sign $\pm 1$ prescribed such that the oppositely charged plates a…

math.CA2017

Condensers with touching plates and constrained minimum Riesz and Green energy problems

P. D. Dragnev, B. Fuglede, D. P. Hardin +2

We study minimum energy problems relative to the $α$ -Riesz kernel $∣ x - y ∣^{α - n}$ , $α \in (0, 2]$ , over signed Radon measures $μ$ on $R^{n}$ , $n ⩾ 3$ , associated with a gene…

math.CA2017★ 2 cited

Constrained minimum Riesz energy problems for a condenser with intersecting plates

P. D. Dragnev, B. Fuglede, D. P. Hardin +2

We study the constrained minimum energy problem with an external field relative to the $α$ -Riesz kernel $∣ x - y ∣^{α - n}$ of order $α \in (0, n)$ for a generalized condenser $\mathbf A=(A…

math.CV2017

Domains of existence for finely holomorphic functions

Bent Fuglede, Alan Groot, Jan Wiegerinck

We show that fine domains in $C$ with the property that they are Euclidean $F_{σ}$ and $G_{δ}$ , are in fact fine domains of existence for finely holomorphic functions. Moreove…

math.CA2016

Balayage for Riesz kernels with application to potential theory for the associated Green kernels

Bent Fuglede, Natalia Zorii

We study properties of the $α$ -Green kernel $g_{D}^{α}$ of order $0 < α ⩽ 2$ for a domain $D \subset R^{n}$ , $n ⩾ 3$ . This kernel is associated with the $α$ -Riesz kernel…

math.CA2016

Symmetric function kernels and sweeping of measures

Bent Fuglede

This is a potential theoretic study of balayage (sweeping) of a positive Radon measure on a locally compact (Hausdorff) space onto a closed, or more generally a quasiclosed set (th…

math.CA2015

Minimum Riesz energy problems for a condenser with "touching plates"

P. D. Dragnev, D. Hardin, E. B. Saff +1

Minimum Riesz energy problems in the presence of an external field are analyzed for a condenser with touching plates. We obtain sufficient and/or necessary conditions for the solva…

math.AP2014

The Dirichlet problem at the Martin boundary of a fine domain

Mohamed El Kadiri, Bent Fuglede

We develop the Perron-Wiener-Brelot method of solving the Dirichlet problem at the Martin boundary of a fine domain in $\RR^n$ ( $n \geq 2$ ).

math.AP2014★ 1 cited

Sweeping at the Martin boundary of a fine domain

Mohamed El Kadiri, Bent Fuglede

We study sweeping on a subset of the Riesz-Martin space of a fine domain in $\RR^n$ ( $n \geq 2$ ), both with respect to the natural topology and the minimal-fine topology, and show tha…

math.AP2014★ 2 cited

Martin boundary of a fine domain and a Fatou-Naim-Doob theorem for finely superharmonic functions

Mohamed El Kadiri, Bent Fuglede

We construct the Martin compactification $U ˉ$ of a fine domain $U$ in $R^{n}$ , $n \geq 2$ , and the Riesz-Martin kernel $K$ on $U \times U ˉ$ . We obtain the integral represent…

math.CV2010

Plurisubharmonic and holomorphic functions relative to the plurifine topology

Mohamed El Kadiri, Bent Fuglede, Jan Wiegerinck

A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A fun…