A Note on the approximation of plurisubharmonic functions

Slimane Benelkourchi

doi:10.1016/j.crma.2006.03.002

Complex Analysis

A Note on the approximation of plurisubharmonic functions
[Sur l'approximation des fonctions plurisousharmoniques]

Présenté par : Pierre Lelong

Slimane Benelkourchi ¹

¹ Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden

Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 647-650.

Résumé
Abstract

Soit $Ω ⋐ C^{n}$ un domaine fortement hyperconvexe et $Ω_{j}$ une suite décroissante de domaines hyperconvexes tel que $Ω = (⋂ Ω_{j}) °$ . On prouve que toute fonction plurisousharmonique $φ \in F^{a} (Ω)$ est limite d'une suite croissante de fonctions $φ_{j} \in F^{a} (Ω_{j})$ .

Let $Ω ⋐ C^{n}$ be a strongly hyperconvex domain and $Ω_{j}$ be a decreasing sequence of hyperconvex domains such that $Ω = (⋂ Ω_{j}) °$ . We show that every plurisubharmonic function $φ \in F^{a} (Ω)$ is a limit of an increasing sequence of functions $φ_{j} \in F^{a} (Ω_{j})$ .

Reçu le : 2006-01-31
Accepté le : 2006-02-28
Publié le : 2006-04-03

DOI : 10.1016/j.crma.2006.03.002

Affiliations des auteurs :

Slimane Benelkourchi ¹

¹ Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden

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     title = {A {Note} on the approximation of plurisubharmonic functions},
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     pages = {647--650},
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     volume = {342},
     number = {9},
     year = {2006},
     doi = {10.1016/j.crma.2006.03.002},
     language = {en},
}

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Slimane Benelkourchi. A Note on the approximation of plurisubharmonic functions. Comptes Rendus. Mathématique, Volume 342 (2006) no. 9, pp. 647-650. doi : 10.1016/j.crma.2006.03.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.03.002/

Bibliographie
Cité par

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[7] E. Poletsky Approximation of plurisubharmonic functions by multipole Green functions, Trans. Amer. Math. Soc., Volume 355 (2003) no. 4, pp. 1579-1591

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