A counterexample to uniform approximation on totally real manifolds in \(\mathbb C^{3}\)
type: Item
instance of: scholarly article
title: A counterexample to uniform approximation on totally real manifolds in \(\mathbb C^{3}\)
zbMATH Open document ID: 1193.32008
author: Erlend Fornæss Wold
published in: Michigan Mathematical Journal
publication date: 2009-12-15T00:00:00Z
review text: The author constructs an example, which proves the following theorem: There exists a proper \(\mathbb{C}^{\infty}\)-smooth embedding \(\phi: \mathbb{R}^{2} \rightarrow \mathbb{C}^{3}\) such that \(M:=\phi(\mathbb{R}^{2})\) is totally real and polynomially convex and yet \(M\) does not admit uniform approximation.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 32E30
Mathematics Subject Classification ID: 32E20
zbMATH DE Number: 5648484
zbMATH Keywords: polynomial convexity
zbMATH Keywords: totally real
zbMATH Keywords: uniform approximation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1250169068
OpenAlex ID: W2042129270
Wikidata QID: Q124936543
cites work: A Carleman theorem for curves in $\mathsf{C}^n$
cites work: Several Complex Variables and Banach Algebras
cites work: Approximation On Arcs and Dendrites Going to Infinity in ℂn
cites work: Eine Verschärfung eines Approximationssatzes von Carleman
cites work: Uniform Approximation on Compact Sets in $\mathsf{C}^n$.
cites work: Q4694612
cites work: Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn
cites work: Approximation theory on totally real submanifolds
cites work: C\(^k\) approximation by holomorphic functions and \(\bar \partial\)-closed forms on C\(^k\) submanifolds of a complex manifold
cites work: Uniform approximation by entire functions
cites work: Uniform approximation on smooth curves
cites work: Polynomial convexity
DOI: 10.1307/MMJ/1250169068
description: scientific article; zbMATH DE number 5648484