Continuity of affine transformations of white noise test functionals and applications
Translations and scalings defined on the Schwartz space of tempered distributions induce continuous transformations on the space of white noise test functionals . 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
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