The \(\overline{\partial}\) problem for \((0,2)\)-forms in infinite dimensional complex spaces
type: Item
instance of: scholarly article
title: The \(\overline{\partial}\) problem for \((0,2)\)-forms in infinite dimensional complex spaces
zbMATH Open document ID: 0967.32035
author: Kwang Ho Shon
author: Jinkee Lee
published in: Proceedings of the Japan Academy. Series A
publication date: 2001-08-26T00:00:00Z
review text: Let \(E\) be a nuclear DF space and \(\Omega \) a pseudoconvex domain in \(E\). Let \(f:\Omega \rightarrow \Lambda^{(0,2)}(E)\) be a holomorphic \((0,2)\)-form. It is shown that there exists a \(\mathcal C^{\infty }\) \((0,1)\)-form \(g\) on \(\Omega \) such that \(\overline \partial g = f.\) For the proof of this result the authors use a corresponding result on separable Hilbert spaces and a certain approximation theorem for holomorphic functions on Hilbert spaces.
Mathematics Subject Classification ID: 32W05
Mathematics Subject Classification ID: 46T25
Mathematics Subject Classification ID: 46G20
zbMATH DE Number: 1335031
zbMATH Keywords: \(\overline\partial\) problem
zbMATH Keywords: nuclear spaces
reviewed by: Fritz Haslinger
MaRDI profile type: Publication
full work available at URL: pjaa.75.35
OpenAlex ID: W1968550905
cites work: Q3840024
cites work: The \(\bar\partial\)-problem for holomorphic (0,2)-forms on pseudoconvex domains in separable Hilbert spaces and D. F. N. spaces
cites work: Q3925393
cites work: Q4066086
cites work: The \(\bar\partial\)-problem for a (0,2)-form in a D.F.N. space
DOI: 10.3792/PJAA.75.35
description: scientific article; zbMATH DE number 1335031