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Beatson, R.K.* ; zu Castell, W.

Dimension hopping and families of strictly positive definite zonal basis functions on spheres.

J. Approx. Theory 221, 22-37 (2017)
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Positive definite functions of compact support are widely used for radial basis function approximation as well as for estimation of spatial processes in geostatistics. Several constructions of such functions for RdRd are based upon recurrence operators. These map functions of such type in a given space dimension onto similar ones in a space of lower or higher dimension. We provide analogs of these dimension hopping operators for positive definite, and strictly positive definite, zonal functions on the sphere. These operators are then used to provide new families of strictly positive definite functions with local support on the sphere.
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Publication type Article: Journal article
Document type Scientific Article
Keywords Zonal functions; Positive definite; Dimension hopping operators; Operators
ISSN (print) / ISBN 0021-9045
e-ISSN 1096-0430
Quellenangaben Volume: 221, Issue: , Pages: 22-37 Article Number: , Supplement: ,
Publisher Elsevier
Publishing Place San Diego
Reviewing status Peer reviewed