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pro vyhledávání: '"Kadiri, Mohamed El"'
Autor:
Kadiri, Mohamed El
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-Amp\`ere operator on a domain set $D\subset \mathbb{C}^n$ ($n\geq 1$) are such that $u_1= v_1, .
Externí odkaz:
http://arxiv.org/abs/2310.10367
Autor:
Kadiri, Mohamed El
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 $U\subset \mathbb{C}^n$, $n\geq 1$, is of the form $U=\bigcup \{\varphi_j>-1\}$, where each $\phi_j$ is a
Externí odkaz:
http://arxiv.org/abs/2309.03391
Autor:
Kadiri, Mohamed El
Let $(u_j)$ be a deaceasing sequence of psh functions in the domain of definition $\cal D$ of the Monge-Amp\`ere operator on a domain $\Omega$ of $\mathbb{C}^n$ such that $u=\inf_j u_j$ is plurisubharmonic on $\Omega$. In this paper we are interested
Externí odkaz:
http://arxiv.org/abs/2301.09495
Autor:
Kadiri, Mohamed El
Let $u$ and $v$ be two plurisubharmonic functions in the domain of definition of the Monge-Amp\`ere operator on a domain $\Omega\subset {\bf C}^n$. We prove that if $u=v$ on a plurifinely open set $U\subset \Omega$ that is Borel measurable, then $(dd
Externí odkaz:
http://arxiv.org/abs/2207.13610
Autor:
Kadiri, Mohamed El
In this note we study the plurifinely locally maximal plurifinely plurisubharmonic functions and improve some known results on these functions. We prove in particular that any locally bounded plurifinely locally maximal plurifinely plurisubharmonic f
Externí odkaz:
http://arxiv.org/abs/1711.00966
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 that this kernel does not always exist. We then introduce and study th
Externí odkaz:
http://arxiv.org/abs/1606.06397
We prove a convergence property for some families of finely harmonic functions on a fine domain $U$ of $\RR^n$ ($n\ge 2$), and we apply it to prove some regularity of the fine Green kernel of $U$.
Comment: 8 pages, in French
Comment: 8 pages, in French
Externí odkaz:
http://arxiv.org/abs/1504.01447
Autor:
Kadiri, Mohamed El, Fuglede, Bent
We develop the Perron-Wiener-Brelot method of solving the Dirichlet problem at the Martin boundary of a fine domain in $\RR^n$ ($n\ge2$).
Externí odkaz:
http://arxiv.org/abs/1501.00209
Autor:
Kadiri, Mohamed El, Fuglede, Bent
We study sweeping on a subset of the Riesz-Martin space of a fine domain in $\RR^n$ ($n\ge2$), both with respect to the natural topology and the minimal-fine topology, and show that the two notions of sweeping are identical.
Comment: Minor corre
Comment: Minor corre
Externí odkaz:
http://arxiv.org/abs/1409.7098
Autor:
Kadiri, Mohamed El, Fuglede, Bent
We construct the Martin compactification ${\bar U}$ of a fine domain $U$ in $R^n$, $n\ge 2$, and the Riesz-Martin kernel $K$ on $U \times{\bar U}$. We obtain the integral representation of finely superharmonic fonctions $\ge 0$ on $U$ in terms of $K$
Externí odkaz:
http://arxiv.org/abs/1403.0857