Recovery of functions by interpolation and sampling
type: Item
instance of: scholarly article
title: Recovery of functions by interpolation and sampling
zbMATH Open document ID: 0871.47017
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-07-14T00:00:00Z
review text: The paper deals with recovering of an arbitrary element \(x\) in a normed space \(X\) from its values \((\phi_n(x))^\infty_{n=1}\) of a sequence of linear functionals \((\phi_n)_{n=1}^\infty\). The operators \(T_n:\mathbb{C}^n\to X\), \(n=1,2,3,\dots\) are said to be recovery operators, if \(|T_n(\phi_1(x),\dots,\phi_n(x))-x|\to 0\) for all \(x\in X\). The authors give some general results on the existence of recovery operators in normed space with particular reference to minimal norm interpolation. The question of whether recovery operators can be linear is studied as well. This is related to an already-studied case, the disk algebra. Also, the question of sampling of band-limited functions is discussed. The author shows how a result of Beurling can be used to construct recovery operators for sampling even in the presence of noise.
Mathematics Subject Classification ID: 47A57
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 902503
zbMATH Keywords: sequence of linear functionals
zbMATH Keywords: recovery operators
zbMATH Keywords: minimal norm interpolation
zbMATH Keywords: sampling of band-limited functions
zbMATH Keywords: presence of noise
author: Jonathan R. Partington
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0084
OpenAlex ID: W1976764517
Wikidata QID: Q56319493
DOI: 10.1006/JMAA.1996.0084
description: scientific article; zbMATH DE number 902503