Factorization theorems for univariate splines on regular grids
type: Item
instance of: scholarly article
title: Factorization theorems for univariate splines on regular grids
zbMATH Open document ID: 0731.41015
DOI: 10.1007/BF02807218
author: A. Ron
published in: Israel Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: A systematic analysis of the possible factorizations of univariate splines is presented. The author uses some of the techniques known in the multivariate situation together with some new ones to obtain factorization results for univariate splines. These results are used for characterizations of the splines of minimal support and singular exponential B-splines. The main factorization theorem can be stated as follows: Let \(\phi\) be a given univariate compactly supported distribution. Denote by S(\(\phi\)) the space spanned by its integer translates, by H(\(\phi\)) the subspace of all exponentials in S(\(\phi\)) and by \(K_{\phi}\) the kernel of the associated semi-discrete convolution \(\phi^*\). Then \(\phi\) can be expressed as \(\phi =\rho (\nabla)\tau *M\), where \(\rho\) (\(\nabla)\) is a finite difference operator, \(\tau\) is a distribution of smaller support satisfying \(H(\tau)=K_{\tau}=\{0\}\), and M is a spline which depends on H(\(\phi\)) but not on \(\phi\) itself.
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 4208738
zbMATH Keywords: univariate splines
zbMATH Keywords: singular exponential B-splines
reviewed by: Georgi R. Grozev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02807218
OpenAlex ID: W2024564324
description: scientific article; zbMATH DE number 4208738