On the dependence of uniform polyanalytic polynomial approximations on the order of polyanalyticity
type: Item
instance of: scholarly article
title: On the dependence of uniform polyanalytic polynomial approximations on the order of polyanalyticity
zbMATH Open document ID: 1175.30004
DOI: 10.1134/S0001434608010045
author: K. Yu. Fedorovskii
author: Joan Josep Carmona
published in: Mathematical Notes
publication date: 2008-10-16T00:00:00Z
review text: Let \(U\) be an open subset of the complex plane \(\mathbb{C}.\) A function \(f\) is said to be n-analytic in \(U\) if it is of the form \(f(z)=\overline z^{n-1} f_{n-1}(z) + \dots + \overline z f_1(z) + f_0(z),\) where \(n\in \mathbb{N}\) and \(f_0,f_1,\dots , f_{n-1}\) are holomorphic functions in \(U.\) For a compact subset \(X\) in \(\mathbb{C}\) let \(P_n(X)\) denote the closure in \(\mathcal{C}(X)\) of the set of all n-analytic polynomials. It is shown that for each integer \(n\geq 1\) there exists a compact set \(X\subset \mathbb{C}\) such that \(P_{2n}(X)=\mathcal{C}(X)\neq P_n(X).\)
reviewed by: Fritz Haslinger
Mathematics Subject Classification ID: 30B60
Mathematics Subject Classification ID: 30C10
zbMATH DE Number: 5352314
zbMATH Keywords: polyanalytic function
zbMATH Keywords: uniform approximation
MaRDI profile type: Publication
cites work: On some properties and examples of Nevanlinna domains
cites work: On uniform approximation by $ n$-analytic functions on closed sets in $ \mathbb C$
cites work: Q3374393
cites work: Q4044857
full work available at URL: s0001434608010045
OpenAlex ID: W2042640182
Recommended article: Q5265126
Recommended article: New conditions for uniform approximation by polyanalytic polynomials
Recommended article: On uniform approximations by polyanalytic polynomials on compact subsets of the plane
Recommended article: Order of uniform approximation by polynomial interpolation in the complex plane and beyond
Recommended article: Q4463734
Recommended article: Q5462321
Recommended article: On the uniform approximation of analytic functions by means of interpolation polynomials
Recommended article: On the relationship between the rate of polynomial approximation of an entire function and its order and type
Recommended article: Uniform \(n\)-analytic polynomial approximations of functions on rectifiable contours in \(\mathbb{C}\)
Recommended article: Uniform polynomial approximation of analytic functions on a quasidisk
description: scientific article; zbMATH DE number 5352314