Order of approximation by electrostatic fields due to electrons
type: Item
instance of: scholarly article
title: Order of approximation by electrostatic fields due to electrons
zbMATH Open document ID: 0584.41007
DOI: 10.1007/BF01890026
author: Xiechang Shen
author: Charles K. Chui
published in: Constructive Approximation
publication date: 1985-01-01T00:00:00Z
review text: Let D be a Jordan domain in the complex plane and \(A_ q(D)\) the Bers space with norm \(\|\) \(\|_ q\). If D is the unit disk, it is known that \(\| S_ n\|_ 2\geq \pi /18\), where \(S_ n=\sum^{n}_{k=1}1/(z-z_{nk})\) with \(z_{nk}\in \partial D\), so that approximation in \(\|\) \(\|_ q\), \(q\leq 2\), is not possible. In this paper, we give an order of estimate of \(\| f-S_ n\|_ q\) for \(2<q<\infty\) when \(\partial D\) is a sufficiently smooth Jordan curve, and prove that this order of approximation is in general best possible.
Mathematics Subject Classification ID: 41A25
Mathematics Subject Classification ID: 41A20
Mathematics Subject Classification ID: 30E10
zbMATH DE Number: 3935661
zbMATH Keywords: Jordan domain
zbMATH Keywords: Bers space
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01890026
OpenAlex ID: W2000421629
description: scientific article; zbMATH DE number 3935661