Title

Continuity of affine transformations of white noise test functionals and applications

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

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