On Gleason's decomposition for \(A^{\infty}(\bar D)\)
type: Item
instance of: scholarly article
title: On Gleason's decomposition for \(A^{\infty}(\bar D)\)
zbMATH Open document ID: 0595.32019
DOI: 10.1007/BF01161921
published in: Mathematische Zeitschrift
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173854
review text: Let D be a bounded pseudoconvex domain in \({\mathbb{C}}^ n\) with \(C^{\infty}\)-boundary. Let \(A^{\infty}(\bar D)\) be the algebra of holomorphic functions in D having derivatives of all orders continuous up to the boundary. The author proves that for each \(f\in A^{\infty}(\bar D)\) there is a decomposition \(f(z)-f(w)=\sum^{n}_{i=1}g_ i(z,w)(z_ i-w_ i)\) with \(g_ i\in A^{\infty}(\bar D\times \bar D)\). The result is in general not true for an arbitrary domain in \({\mathbb{C}}^ n\).
Mathematics Subject Classification ID: 32A38
Mathematics Subject Classification ID: 32A40
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 3957608
zbMATH Keywords: pseudoconvex domain
zbMATH Keywords: algebra of holomorphic functions
zbMATH Keywords: Gleason decomposition
author: J. M. Ortega
MaRDI profile type: Publication
cites work: Q5617018
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description: scientific article; zbMATH DE number 3957608