Riesz bases of splines and regularized splines with multiple knots
type: Item
instance of: scholarly article
title: Riesz bases of splines and regularized splines with multiple knots
zbMATH Open document ID: 0876.41009
published in: Journal of Approximation Theory
publication date: 1997-02-20T00:00:00Z
review text: The authors prove several \(L_2\)- and Sobolev-norm stability results on the real line. First, they consider \(B\)-splines of order \(m\), defined on a bi-infinite knot sequence, where each knot is allowed to have a multiplicity of at most \(m\), and they prove a stability result for \(B\)-spline series in certain Sobolev-norms. Then they discuss generalizations of \(B\)-splines defined via their Fourier transforms using tempered distributions. A Riesz-basis property for such regularized splines is established, both in \(L_2\)- and in Sobolev-norms, under certain technical assumptions. Finally, the stability of scattered Hermite interpolation on the real line is investigated in this context.
Mathematics Subject Classification ID: 41A15
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 980677
zbMATH Keywords: stability
zbMATH Keywords: \(B\)-splines with multiple knots
zbMATH Keywords: regularized splines
zbMATH Keywords: Riesz basis
author: K. Jetter
author: Joachim Stöckler
reviewed by: E. Quak
MaRDI profile type: Publication
full work available at URL: jath.1996.0108
OpenAlex ID: W2017257439
DOI: 10.1006/JATH.1996.0108
description: scientific article; zbMATH DE number 980677