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
Conditionally Positive Definite Functions and Laplace-Stieltjes Integrals
β Scribed by K. Guo; S. Hu; X. Sun
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 460 KB
- Volume
- 74
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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
## JHctfy -An algorithiii is proposed for estimating the value of a definite integral in a regression model, subject to the constraint that increasing the value of any observation does not decrease the estimated value of the integral. It is shown t h a t the estimator is consistent and asymptotica