Characteristic functional of a probability measure absolutely continuous with respect to a Gaussian Radon measure
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).
scientific article; zbMATH DE number 4000282
scientific article