The density of translates of zonal kernels on compact homogeneous spaces
type: Item
instance of: scholarly article
title: The density of translates of zonal kernels on compact homogeneous spaces
zbMATH Open document ID: 0947.41017
author: D. L. Ragozin
author: Jeremy Levesley
published in: Journal of Approximation Theory
publication date: 2000-07-24T00:00:00Z
review text: Classes of functions were studied which relate to approximation or to analysis of the approximating properties of other classes of functions. For quasi-interpolation the real symmetric (or self-adjoint) kernel \(k(x,y)\) and the approximating properties of linear combinations \(\sum a_i k(x,y)\) were analyzed. To this aim the density properties of such linear combinations are needed. The paper investigates the density properties of such linear combinations and shows how to use the density of polynomials to determine the kernel \({\mathcal K}\) for specific \(k\) forms. The kernel function generalizes the idea of a radial or distance-dependent function on spheres or tori. The \(G\)-invariant polynomial decomposition of \(L^2\) and the reduction of zonal kernel operators was discussed.
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 1443204
zbMATH Keywords: approximation by special functions
zbMATH Keywords: approximation by polynomials
zbMATH Keywords: degree of approximation
MaRDI profile type: Publication
OpenAlex ID: W1984393031
cites work: Q5543516
cites work: Q3331943
cites work: Generalised sk-spline interpolation on compact abelian groups
cites work: Q5557165
cites work: Spherical harmonics
cites work: Positive definite functions on spheres
cites work: The fundamentality of translates of a continuous function on spheres
cites work: Fundamental sets of continuous functions on spheres
DOI: 10.1006/JATH.1999.3432
description: scientific article; zbMATH DE number 1443204