On the smoothness of positive definite and radial functions

Wendland, Holger (1999) On the smoothness of positive definite and radial functions. Journal of Computational and Applied Mathematics, 101 (1-2). pp. 177-188. ISSN 0377-0427

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Abstract

We consider positivedefinite and radialfunctions. After giving general results concerning the smoothness of general positivedefinite and radialfunctions, we investigate the class of compactly supported, positivedefinite, and radialfunctions, where every function consists of a univariate polynomial within its support. Especially, we show that these functions necessarily possess an even number of continuous derivatives. Finally, we provide a general construction technique which we use to construct a new family of compactly supported basis functions of arbitrary smoothness.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Holger Wendland
Date Deposited: 06 Feb 2012 20:46
Last Modified: 10 Jul 2012 11:35
URI: http://sro.sussex.ac.uk/id/eprint/27993
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