On the smoothness of positive de nite and radial functions
نویسنده
چکیده
We consider positive de nite and radial functions. After giving general results concerning the smoothness of general positive de nite and radial functions, we investigate the class of compactly supported, positive de nite, and radial functions, 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. c © 1999 Elsevier Science B.V. All rights reserved.
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تاریخ انتشار 1998