Abstract
We discuss different representations of the white noise test functions (E)β , 0 ≤ β < 1 by introducing generalized Wick tensors. As an application we state the following generalization of the Mehler formula for the Ornstein-Uhlenbeck semigroup, see [7, p. 237]: Let a, b ∈ C, 0 ≤ β < 1. Then a · ∆G + b · N is the infinitesimal generator of the following regular differentiable one parameter transformation group { Pa,b,t } t∈R ⊂ GL((E)β): (i) if b = 0 then for all φ ∈ (E)β , t ∈ R :
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