Recurrence relations for radial positive definite functions
type: Item
instance of: scholarly article
title: Recurrence relations for radial positive definite functions
zbMATH Open document ID: 1014.42007
DOI: 10.1016/S0022-247X(02)00101-4
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: In the theory of radial basis functions as well as in the theory of spherically symmetric characteristic functions, recurrence relations are used to construct \(d\)-dimensional functions starting with lower-dimensional ones. The author shows that the operators used so far are special cases of one-step recurrence relations for \(\ell_2\)-radial positive definite functions. He further gives the analogue for \(\ell_1\)-radial functions and thereby defines a turning bands operator for 1-symmetric characteristic functions.
Mathematics Subject Classification ID: 42A82
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 33C90
Mathematics Subject Classification ID: 43A35
zbMATH DE Number: 1836742
zbMATH Keywords: radial positive definite functions
zbMATH Keywords: spherically symmetric characteristic functions
zbMATH Keywords: recurrence relations
zbMATH Keywords: turning bands operator
author: Wolfgang zu Castell
reviewed by: H. M. Srivastava
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00101-4
OpenAlex ID: W2039464386
description: scientific article; zbMATH DE number 1836742