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Beatson, R.K.* ; zu Castell, W. ; Xu, Y.*

A Pólya criterion for (strict) positive-definiteness on the sphere.

IMA J. Numer. Anal. 34, 550-568 (2014)
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Positive-definite functions are very important in both the theory and applications of approximation theory, probability and statistics. In particular, identifying strictly positive-definite kernels is of great interest as interpolation problems based upon such kernels are guaranteed to have a unique solution whenever the nodes {xj} are distinct. A Bochner-type result of Schoenberg characterizes continuous positive-definite zonal functions, f(cos ·), on the sphere
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Publication type Article: Journal article
Document type Scientific Article
Keywords positive-definite functions; strictly positive-definite; Polya criterion; sphere; compactly supported kernel; Polynomials; Zeros
ISSN (print) / ISBN 0272-4979
e-ISSN 1464-3642
Quellenangaben Volume: 34, Issue: 2, Pages: 550-568 Article Number: , Supplement: ,
Publisher Oxford University Press
Publishing Place Oxford
Reviewing status Peer reviewed