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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     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

[1] E. Bedford; B.A. Taylor A new capacity for plurisubharmonic functions, Acta Math., Volume 149 (1982), pp. 1-40

[2] S. Benelkourchi; B. Jennane; A. Zeriahi Polya's inequalities, global uniform integrability and the size of plurisubharmonic lemniscates, Ark. Mat., Volume 43 (2005), pp. 85-112

[3] U. Cegrell, Personal communication, 2005

[4] U. Cegrell The general definition of the Monge–Ampère operator, Ann. Inst. Fourier (Grenoble), Volume 54 (2004) no. 1, pp. 159-179

[5] U. Cegrell; S. Kolodziej; A. Zeriahi Subextension of plurisubharmonic functions with weak singularities, Math. Z., Volume 250 (2005), pp. 7-22

[6] S. Kolodziej The complex Monge–Ampère equation, Acta Math., Volume 180 (1998), pp. 69-117

[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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