𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On the smoothness of positive definite and radial functions

✍ Scribed by Holger Wendland

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
596 KB
Volume
101
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

✦ Synopsis

We consider positive definite and radial functions. After giving general results concerning the smoothness of general positive definite and radial functions, we investigate the class of compactly supported, positive definite, 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.

πŸ“œ SIMILAR VOLUMES

Addendum to the Paper β€žOn the Measurabil
Addendum to the Paper β€žOn the Measurability of Positive Definite and Conditionally Positive Definite Functions”
✍ ZoltΓ‘n SasvΓ‘ri πŸ“‚ Article πŸ“… 1987 πŸ› John Wiley and Sons 🌐 English βš– 116 KB πŸ‘ 1 views

Let f be a positive definite function on a locally compact abelian group G. In [3] we showed that measurability of 1 on an open neighbourhood of the zero implies measurability of f on G. As a main tool we used a result about the support of f [3, Th. I]. The aim of this note is to simplify the proof

On Continuity and Decomposition of Posit
On Continuity and Decomposition of Positive Definite Functions
✍ ZoltΓ‘n SasvΓ‘ri πŸ“‚ Article πŸ“… 1989 πŸ› John Wiley and Sons 🌐 English βš– 329 KB

Let G be a locally compact commutative group and let g and h be positive definite functions on G, which are not identically zero. We show that continuity of gh implies the existence of a character y of Gd (the discrete version of G) such that yg and y h are continuous. As corollary we get a special