• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.527-538
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• 1998

We study on kernel operators (Wick monomials) on symmetric Fock space. We give optimal conditions on kernels so that the corresponding kernel operators are densely defined linear operators on the Fock space. We try to formulate our results in the framework of white noise analysis as much as possible. The most of the results in this paper can be extended to anti-symmetric Fock space.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.329-336
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• 1999

We construct the Gelfand triple based on the space \ulcorner, introduced by Sato and di Silva, of analytic and exponentially decreasing function. This space denoted by(\ulcorner) of white noise test functionals are defined by the operator cosh \ulcorner, A=-(\ulcorner)\ulcorner+x\ulcorner+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.