Traces of pluriharmonic functions on curves
type: Item
instance of: scholarly article
title: Traces of pluriharmonic functions on curves
zbMATH Open document ID: 0727.31005
DOI: 10.1007/BF02387377
author: Bo Berndtsson
author: Joaquim Bruna
published in: Arkiv för Matematik
publication date: 1990-01-01T00:00:00Z
review text: Let \(B_ n\) be the unit ball in \(C^ n\), S its boundary, and \(\gamma\) a simple smooth curve in S; it is well known that \(\gamma\) is an interpolation set for the ball algebra (that is every continuous function on \(\gamma\) is the restriction of a function holomorphic in \(B_ n\) and continuous on \(\bar B_ n)\) if and only if at each point of \(\gamma\), the tangent vector lies in the complex tangent space of S at that point. A subset E of S is said to be a set of pluriharmonic (resp. almost pluriharmonic) interpolation if any continuous function on E can be extended to a pluriharmonic function continuous on \(\bar B_ n\) (resp. the space of the restrictions of continuous pluriharmonic functions on \(\bar B_ n\) to E is of finite-codimension in the space of continuous functions on E). The authors' main result is to show that a smooth simple closed curve in S is of almost pluriharmonic interpolation.
reviewed by: Lawrence Gruman
Mathematics Subject Classification ID: 31C10
Mathematics Subject Classification ID: 32U05
zbMATH DE Number: 4200580
zbMATH Keywords: pluriharmonic interpolation
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02387377
OpenAlex ID: W1967604813
description: scientific article; zbMATH DE number 4200580