On the Lévy-Khintchine decomposition of conditionally positive definite functions
✍ Scribed by Herbert Heyer
- Publisher
- Springer Netherlands
- Year
- 2006
- Tongue
- English
- Weight
- 213 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0031-5303
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
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
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