Characteristic functional of a probability measure absolutely continuous with respect to a Gaussian Radon measure
type: Item
instance of: scholarly article
title: Characteristic functional of a probability measure absolutely continuous with respect to a Gaussian Radon measure
zbMATH Open document ID: 0617.28016
DOI: 10.1016/0022-1236(85)90035-7
author: Hiroshi Sato
published in: Journal of Functional Analysis
publication date: 1985-01-01T00:00:00Z
review text: Let \(\mu\) be a Gaussian measure in a locally convex linear topological space E. The author investigates conditions of absolute continuity of a certain Radon measure \(\mu_ 1\) on E with respect to \(\mu\) and states them using characteristic functional of \(\mu_ 1\). The obtained results are made more detailed for the case \(\mu_ 1=\mu \otimes \nu\) is a convolution of \(\mu\) with a measure \(\nu\). Special attention is paid as well to measures generated by a Wiener random process. The investigation is based on Fourier-Wiener transformation properties and its inverse transformation. To obtain more information about Fourier- Wiener transformation see the book by the reviewer and \textit{S. V. Fomin}: ''Measures and differential equations in infinite dimensional spaces'' (1983; Zbl 0536.46031).
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 60B11
zbMATH DE Number: 4000282
zbMATH Keywords: Gaussian measure
zbMATH Keywords: absolute continuity
zbMATH Keywords: Radon measure
zbMATH Keywords: characteristic functional
zbMATH Keywords: Wiener random process
zbMATH Keywords: Fourier-Wiener transformation
MaRDI profile type: Publication
full work available at URL: 0022-1236(85)90035-7
OpenAlex ID: W2017946325
cites work: Q4192725
cites work: Fourier Transforms. (AM-19)
cites work: Gaussian radon measures on locally convex spaces.
cites work: Measurable Functions on Hilbert Space
cites work: Q5526190
cites work: Q4136254
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description: scientific article; zbMATH DE number 4000282