Document Type
Article
Publication Date
1-1-1992
Abstract
Translations and scalings defined on the Schwartz space of tempered distributions induce continuous transformations on the space of white noise test functionals [25]. Continuity of the induced transformations with respect to their parameters is proved. As a consequence one obtains a direct simple proof of the fact that the space of white noise test functionals is infinitely differentiable in Fréchet sense. Moreover, it is shown that the Wiener semigroup acts as a mollifier on the space of test functionals. © 1992.
Publication Source (Journal or Book title)
Stochastic Processes and their Applications
First Page
85
Last Page
98
Recommended Citation
Kuo, H., Potthoff, J., & Yan, J. (1992). Continuity of affine transformations of white noise test functionals and applications. Stochastic Processes and their Applications, 43 (1), 85-98. https://doi.org/10.1016/0304-4149(92)90077-4
