Quasi-interpolation in the Fourier algebra
type: Item
instance of: scholarly article
title: Quasi-interpolation in the Fourier algebra
zbMATH Open document ID: 1108.41006
author: H. G. Feichtinger
author: Norbert Kaiblinger
published in: Journal of Approximation Theory
publication date: 2007-02-14T00:00:00Z
review text: In this paper, the most interesting topic of quasi-interpolation by the so-called Schoenberg operator is studied. This is an important operator especially in univariate and multivariate spline theory, as well as in, for example, the theory of radial basis functions. Here, the convergence of these operators in certain algebras is studied. That is, the convergence in generalisations of \(L^p\)-norms of the approximations generated by these operators to the functions approximated is established. An example for these results is the convergence proof in the Fourier algebra.
reviewed by: Martin D. Buhmann
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 41A63
zbMATH DE Number: 5125996
zbMATH Keywords: Schoenberg operator
zbMATH Keywords: quasi-interpolation
zbMATH Keywords: spline approximation
zbMATH Keywords: Strang-Fix conditions
zbMATH Keywords: Fourier algebra
zbMATH Keywords: Feichtinger's algebra
MaRDI profile type: Publication
full work available at URL: j.jat.2006.05.001
OpenAlex ID: W2169808774
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DOI: 10.1016/J.JAT.2006.05.001
description: scientific article; zbMATH DE number 5125996