White Noise Hyperfunctions
Commun. Korean Math. Soc. 1999 Vol. 14, No. 2, 329-336
Soon-Yeong Chung, Eun Gu Lee
Sogang University, Dongyang Technical College
Abstract : We construct the Gelfand triple based on the space $\Cal G$, introduced by Sato and di Silva, of analytic and exponentially decreasing functions. This space denoted by $(\Cal G)$ of white noise test functionals are defined by the operator $\cosh\sqrt A$, $\displaystyle{A=-\left({d\over dx}\right)^2+x^2+1}$. We also note that many properties like generalizations of the Paley--Wiener theorem and the Bochner--Schwartz theorem hold in this space as in the space of Hida distributions.
Keywords : white noise, hyperfunction
MSC numbers : 46F15, 46F25
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