Continuity of affine transformations of white noise test functionals and applications

H. -H. Kuo, J. Potthoff and J. -A. Yan

Stochastic Processes and their Applications, 1992, vol. 43, issue 1, 85-98

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.

Keywords: white; noise; analysis; affine; transformation; Wiener; semigroup; Frechet; derivative; Hida; distribution; test; functional (search for similar items in EconPapers)
Date: 1992
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