Abstract
In this paper we present recent results on infinite dimensional Laplacians. In particular, by introducing the operator which transfers regular white noise functionals to functionals of exponential white noise, we give a relationship between an infinite dimensional Fourier-Mehler transform and the Levy Laplacian. The operator implies a Gauss-Poisson correspondence if we consider the Levy Laplacian acting on multiple Wiener integrals by some Levy process. We also give an infinite dimensional random field associated with the Levy Laplacian.
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