Smooth regularization of plurisubharmonic functions
type: Item
instance of: scholarly article
title: Smooth regularization of plurisubharmonic functions
zbMATH Open document ID: 0919.31003
DOI: 10.1007/BF02355913
author: R. S. Yulmukhametov
published in: Mathematical Notes
publication date: 1999-07-28T00:00:00Z
review text: A new regularization (smoothing) method for plurisubharmonic functions is proposed. Being applied to a plurisubharmonic function \(u\) in a pseudoconvex domain \(G\subset \mathbb{C}^n\), it produces a sequence of functions \(u_j\in \text{PSH} (G)\cap C^\infty(G)\) decreasing to \(u\). Furthermore, a function \(u\in \text{PSH} (\mathbb{C}^n)\) of finite order \(\rho>0\) can be approximated by a smooth plurisubharmonic function \(v\) such that \(| u-v|\) has almost logarithmic or power-law growth outside a small set \(E\subset \mathbb{C}^n\). In the latter case, \(|\text{grad } v|\) has power-law bounds, too. As a consequence, \(u\) is approximated by \(\log| f|\) with \(f\) an entire function, such that \[ \bigl| u(z)- \log| f(z)| \bigr|\leq C_\alpha(1+| z|)^\alpha, \quad z\not\in E, \] with any \(\alpha> \frac 45 \rho\).
Mathematics Subject Classification ID: 31C10
Mathematics Subject Classification ID: 32U05
zbMATH DE Number: 1257029
zbMATH Keywords: approximation
zbMATH Keywords: regularization
zbMATH Keywords: smoothing
zbMATH Keywords: plurisubharmonic functions
MaRDI profile type: Publication
cites work: Q5631423
cites work: Asymptotics of the difference of subharmonic functions
cites work: Q3708270
Recommended article: Smoothing plurisubharmonic functions on complex spaces
Recommended article: Plurisubharmonic functions on smooth domains.
Recommended article: On regularization of plurisubharmonic functions on manifolds
Recommended article: On smoothing of plurisubharmonic functions on unbounded domains
Recommended article: On the regularization of \(J\)-plurisubharmonic functions
Recommended article: On regularization of plurisubharmonic functions near boundary points
Recommended article: Regularization of quasi-plurisubharmonic functions on complex manifolds
Recommended article: Smooth approximation of plurisubharmonic functions on almost complex manifolds
Recommended article: Smooth plurisubharmonic functions without subextension
description: scientific article; zbMATH DE number 1257029