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

Presented by: 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

Abstract (Original language)
Résumé

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 $φ_{j} \in F^{a} (Ω_{j})$ .

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 $φ_{j} \in F^{a} (Ω_{j})$ .

Received: 2006-01-31
Accepted: 2006-02-28
Published online: 2006-04-03

DOI: 10.1016/j.crma.2006.03.002

Author's affiliations:

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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     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

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