On \(L_ p\)-boundedness of the \(L_ 2\)-projector onto splines
type: Item
instance of: scholarly article
title: On \(L_ p\)-boundedness of the \(L_ 2\)-projector onto splines
zbMATH Open document ID: 0806.41010
author: A. Shadrin
published in: Journal of Approximation Theory
publication date: 1994-10-10T00:00:00Z
review text: Let \(\Delta_ n= \{a= t_ 0< t_ 1<\cdots< t_ n= b\}\) be a partition of the interval \([a,b]\), \(S_{m-1}(\Delta_ n)\) be the space of splines of degree \(m-1\) with deficiency 1 on the mesh \(\Delta_ n\), \(P_ S\) be an orthogonal projection onto \(S_{m-1}(\Delta_ n)\) defined by \[ \int^ b_ a [f(t)- P_ S(f,t)] \sigma(t) dt\quad \forall\sigma\in S_{m-1}(\Delta_ n). \] It is proved that the \(L_ p\)-norm of the operator \(P_ S\) is uniformly bounded for any mesh \(\Delta_ n\) at least for \(p\) close to 2 and that it is uniformly bounded for all \(p\in [1,\infty]\) in meshes \(\Delta_ n\) with a fixed number of nodes \(n\).
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 636074
zbMATH Keywords: \(L^ 2\)-projectors
zbMATH Keywords: \(L^ p\)-estimates
zbMATH Keywords: splines
reviewed by: Boris Rubin
MaRDI profile type: Publication
full work available at URL: jath.1994.1054
OpenAlex ID: W2141077182
DOI: 10.1006/JATH.1994.1054
description: scientific article; zbMATH DE number 636074