M. El Kadiri

activity

20122023

most citedMaximal Plurifinely Plurisubharmonic functions

21 citations · 24 across the 9 of their papers we have counts for

collaborators

10 papers

math.CV2023

A note on equality on plurifinely open sets of some complex Monge-Ampère measures

Mohamed El Kadiri

Our aim in this paper is to prove that if plurisubharmonic functions $u_{1}, ..., u_{n}$ , $v_{1}, ..., v_{n}$ in the domain of definition of the complex Monge-Ampère operator on a domai…

math.CV2023

A note on the structure of plurifinely open sets and the equality of some complex Monge-Ampère measures

Mohamed El Kadiri

In a recent preprint published on arXiv (see arXiv:2308.02993v2, referred here as \cite{NXH}), N.X. Hong stated that every plurifinely open set $U \subset C^{n}$ , $n \geq 1$ ,…

math.CV2023

Remarks on weak convergence of complex Monge-Ampère measures

Mohamed El Kadiri

Let $(u_{j})$ be a deaceasing sequence of psh functions in the domain of definition $D$ of the Monge-Ampère operator on a domain $Ω$ of $C^{n}$ such that $u = in f_{j} u_{j}$ i…

math.CV2022

An equality of Monge-Ampère measures

Mohamed El Kadiri

Let $u$ and $v$ be two plurisubharmonic functions in the domain of definition of the Monge-Ampère operator on a domain $Ω \subset C^{n}$ . We prove that if $u = v$ on a plurifinely…

math.AP2016

On the existence of the biharmonic Green kernels and the the adjoint biharmonic functions

Abderrahim Aslimani, Imad El Ghazi, Mohamed El Kadiri +1

We study the existence and the regularity of the biharmonic Green kernel in a Brelot biharmonic space whose associated harmonic spaces have Green kernels. We show by some examples…

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.CV2013★ 21 cited

Maximal Plurifinely Plurisubharmonic functions

Mohamed El Kadiri, Iris Marjan Smit

The main purpose of this paper is to introduce and study the notion of plurifinely-maximal plurifinely plurisubharmonic functions, which extends the notion of maximal plurisubharmo…

math.CV2012

Plurifinely Plurisubharmonic functions and the Monge Ampère Operator

Mohamed El Kadiri, Jan Wiegerinck

We will define the Monge-Ampère operator on finite (weakly) plurifinely plurisubharmonic functions in plurifinely open sets in complex n-space and show that it defines a positive m…