On the (bi)infinite case of Shadrin's theorem concerning the \(L_{\infty}\)-boundedness of the \(L_{2}\)-spline projector
type: Item
instance of: scholarly article
title: On the (bi)infinite case of Shadrin's theorem concerning the \(L_{\infty}\)-boundedness of the \(L_{2}\)-spline projector
zbMATH Open document ID: 1298.41016
DOI: 10.1134/S0081543812050082
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2014-09-18T00:00:00Z
review text: \textit{A. Yu. Shadrin} in [Acta Math. 187, No. 1, 59--137 (2001; Zbl 0996.41006)] proved the de Boor conjecture. That is, he proved that the \(L_\infty\) norm of the \(L_2\)-spline projector is bounded independently of the knot sequence. In the present paper the author ties up some loose ends in Shadrin's remarkable proof.
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 6345599
zbMATH Keywords: splines
zbMATH Keywords: \(L_\infty\)-boundedness
zbMATH Keywords: \(L_2\)-spline projector
zbMATH Keywords: totally positive
author: Carl De Boor
reviewed by: Allan Pinkus
MaRDI profile type: Publication
cites work: Structure of invertible (bi)infinite totally positive matrices
cites work: Q5394312
cites work: Q3651574
cites work: The \(L_\infty\)-norm of the \(L_2\)-spline projector is bounded independently of the knot sequence: A proof of de Boor's conjecture
full work available at URL: s0081543812050082
OpenAlex ID: W1986158718
description: scientific article; zbMATH DE number 6345599