Let $\mu$ be a Radon probability measure on a type 2 Banach space $E$. The following Bochner's theorem is proved. For every continuous positive definite function $\phi(\phi(0) = 1)$ on $E$, there exists a Radon probability measure $\sigma_\phi$ on the measurable dual $H_0(\mu)$ of $(E, \mu)$ with the characteristic functional $\phi$ (in some restricted sense).
Publié le : 1985-08-14
Classification:
Bochner's theorem,
measurable dual,
type 2 Banach space,
pre-Gaussian measure,
28C20,
60B11
@article{1176992925,
author = {Okazaki, Yoshiaki},
title = {Bochner's Theorem in Measurable Dual of Type 2 Banach Space},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 1022-1023},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992925}
}
Okazaki, Yoshiaki. Bochner's Theorem in Measurable Dual of Type 2 Banach Space. Ann. Probab., Tome 13 (1985) no. 4, pp. 1022-1023. http://gdmltest.u-ga.fr/item/1176992925/