On the uniform approximation problem for the square of the Cauchy-Riemann operator
type: Item
instance of: scholarly article
title: On the uniform approximation problem for the square of the Cauchy-Riemann operator
zbMATH Open document ID: 0822.30029
author: J. Verdera
published in: Pacific Journal of Mathematics
publication date: 1995-10-04T00:00:00Z
review text: Let \(X\) be a compact subset of the complex plane and \(f\) a continuous function on \(X\) satisfying the differential equation \(\overline \partial^ 2f = 0\) in the interior of \(X\). It is unknown whether \(f\) can be uniformly approximated on \(X\) by functions \(g\) satisfying the equation \(\overline \partial^ 2g = 0\) in some neighborhood (depending on \(g)\) of \(X\). The author shows that this is the case under the additional assumption that \(f\) satisfies a Dini-type continuity condition.
reviewed by: James Li-Ming Wang
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 509122
zbMATH Keywords: uniform approximation
zbMATH Keywords: Cauchy-Riemann operator
MaRDI profile type: Publication
full work available at URL: pjm.1993.159.379
OpenAlex ID: W1532323730
DOI: 10.2140/PJM.1993.159.379
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description: scientific article; zbMATH DE number 509122