Uniform \(n\)-analytic polynomial approximations of functions on rectifiable contours in \(\mathbb{C}\)
type: Item
instance of: scholarly article
title: Uniform \(n\)-analytic polynomial approximations of functions on rectifiable contours in \(\mathbb{C}\)
zbMATH Open document ID: 0879.30021
DOI: 10.1007/BF02308692
published in: Mathematical Notes
publication date: 1997-07-14T00:00:00Z
review text: A complex valued function \(f\) is said to be \(n\)-analytic in the complex domain \(D\) if \(\partial^nf/\partial \overline{z}^n =0\) on \(D\). An \(n\)-analytic polynomial is a polynomial in \(z\) and \(\overline{z}\) that is an \(n\)-analytic function in the whole plane. Let \(X\) be a closed rectifiable Jordan curve in \(\mathbb{C}\) and denote by \(C(X)\) the usual Banach space of continuous complex valued functions on \(X\) with the uniform norm. Using analytic properties, the author characterizes such curves \(X\) for which there exists at least a function in \(C(X)\) that cannot be limit of any sequence of \(n\)-analytic polynomials.
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 1028545
zbMATH Keywords: Mergelyan theorem
zbMATH Keywords: Nevanlinna contour
author: K. Yu. Fedorovskii
reviewed by: Miguel A. Jiménez
MaRDI profile type: Publication
cites work: Q5832207
cites work: Mergelyan's approximation theorem for rational modules
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description: scientific article; zbMATH DE number 1028545