File(s) not publicly available
On the smoothness of positive definite and radial functions
journal contribution
posted on 2023-06-08, 07:43 authored by Holger WendlandWe 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.
History
Publication status
- Published
Journal
Journal of Computational and Applied MathematicsISSN
0377-0427Publisher
ElsevierExternal DOI
Issue
1-2Volume
101Page range
177-188Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC