Constrained Hardy space approximation
type: Item
instance of: scholarly article
title: Constrained Hardy space approximation
zbMATH Open document ID: 1208.41016
author: Arne Schneck
published in: Journal of Approximation Theory
publication date: 2010-09-29T00:00:00Z
full work available at URL: https://publikationen.bibliothek.kit.edu/1000011991
review text: This paper establishes the uniqueness of a solution of a minimization problem for continuous functions defined on a subset of the complex unit circle. The author shows, that for each such \(f\), there is a unique function \(h\) -- in the Hardy space \(H^p\) defined on the complex unit circle and which is also subject to the condition that \(|h| < g\) for some positive function \(g\) -- such that \(\|f-h\|\) is minimal. Moreover, this minimal solution can be approximated by smooth functions.
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 32A35
zbMATH DE Number: 5793308
zbMATH Keywords: unique best approximation
zbMATH Keywords: smooth approximates
reviewed by: Daniel Wulbert
MaRDI profile type: Publication
OpenAlex ID: W2070023494
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DOI: 10.1016/J.JAT.2010.03.006
description: scientific article; zbMATH DE number 5793308