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A remark on the space of testing random variables in the white noise calculus

Published online by Cambridge University Press:  22 January 2016

Izumi Kubo  and
Yoshitaka Yokoi
Izumi Kubo
Affiliation:
Faculty of Integrated Arts and Sciences, Hiroshima University, Hiroshima 730, Japan
Yoshitaka Yokoi
Affiliation:
Department of Mathematics, Faculty of General Education, Kumamoto University, Kumamoto 860, Japan
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The first author and S. Takenaka introduced the structure of a Gel’fand triplet ℋ ⊂ (L2) ⊂ ℋ* into Hida’s calculus on generalized Brownian functionals [4-7]. They showed that the space ℋ of testing random variables has nice properties. For example, ℋ is closed under multiplication of two elements in ℋ, each element of ℋ is a continuous functional on the basic space ℰ*, in addition it can be considered as an analytic functional, and moreover exp [tΔv] (Δv is Volterra’s Laplacian) is real analytic in t ∊ R as a one-parameter group of operators on ℋ, etc.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 115 , September 1989 , pp. 139 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

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