Generalised sk-spline interpolation on compact abelian groups
type: Item
instance of: scholarly article
title: Generalised sk-spline interpolation on compact abelian groups
zbMATH Open document ID: 0922.41002
author: Jeremy Levesley
author: Alexander Kushpel
published in: Journal of Approximation Theory
publication date: 1999-05-26T00:00:00Z
review text: Let \(G\) be a compact abelian metric group, \(\widehat G\) the dual group of \(G\). Let be \(k\in C(G)\). Then an sk-spline is a funktion of the form \(c_0+\sum_{i=1}^{n}c_ik(\dot x_i^{-1})\), where \(n\in\mathbb N\), \(\sum_{i=1}^n c_i=0\), \(x_1,\dots,x_n\in G\). Density of the linear span of sk-splines in \(C(G)\) is proved. The authors also consider interpolation problems for these splines and the problem of the minimization of seminorm \(\int_G| (B^*)^{-1}g(x)| ^2d\mu(x)\), where \(B\) is a continuous linear operator from \((C(G))'\) to \(C(G)\). They also give an estimation of the approximation of convolution classes by sk-splines on \(\mathbb T^d\).
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1278847
zbMATH Keywords: compact abelian group
zbMATH Keywords: sk-splines
MaRDI profile type: Publication
full work available at URL: jath.1997.3267
OpenAlex ID: W2037570824
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DOI: 10.1006/JATH.1997.3267
description: scientific article; zbMATH DE number 1278847