A Note on the approximation of plurisubharmonic functions

Benelkourchi, Slimane

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

Benelkourchi, Slimane ¹

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

Comptes Rendus. Mathématique, Tome 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 :

Benelkourchi, Slimane ¹

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

@article{CRMATH_2006__342_9_647_0,
     author = {Benelkourchi, Slimane},
     title = {A {Note} on the approximation of plurisubharmonic functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {647--650},
     publisher = {Elsevier},
     volume = {342},
     number = {9},
     year = {2006},
     doi = {10.1016/j.crma.2006.03.002},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2006.03.002/}
}

TY  - JOUR
AU  - Benelkourchi, Slimane
TI  - A Note on the approximation of plurisubharmonic functions
JO  - Comptes Rendus. Mathématique
PY  - 2006
SP  - 647
EP  - 650
VL  - 342
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2006.03.002/
DO  - 10.1016/j.crma.2006.03.002
LA  - en
ID  - CRMATH_2006__342_9_647_0
ER  -

%0 Journal Article
%A Benelkourchi, Slimane
%T A Note on the approximation of plurisubharmonic functions
%J Comptes Rendus. Mathématique
%D 2006
%P 647-650
%V 342
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2006.03.002/
%R 10.1016/j.crma.2006.03.002
%G en
%F CRMATH_2006__342_9_647_0

Benelkourchi, Slimane. A Note on the approximation of plurisubharmonic functions. Comptes Rendus. Mathématique, Tome 342 (2006) no. 9, pp. 647-650. doi : 10.1016/j.crma.2006.03.002. http://www.numdam.org/articles/10.1016/j.crma.2006.03.002/

Bibliographie
Cité par

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

[2] Benelkourchi, S.; Jennane, B.; Zeriahi, A. 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] Cegrell, U. The general definition of the Monge–Ampère operator, Ann. Inst. Fourier (Grenoble), Volume 54 (2004) no. 1, pp. 159-179

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

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

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

Cité par Sources :