In this paper we first construct a two-parameter transformation group G on the space of test white noise functionals in which the adjoints of Kuo's Fourier and Kuo's Fourier—Mehler transforms are included. Next we show that the group G is a two-dimensional complex Lie group whose infinitesimal generators are the Gross Laplacian Δ G and the number operator N , and then find an explicit description of a differentiable one-parameter subgroup of G whose infinitesimal generator is aΔ G +bN . As an application, we study the solution and fundamental solution for the Cauchy problem associated with aΔ G +bN . Finally we show that each element of the adjoint group G * of G can be characterized in terms of differentiation and multiplication operators.
Applied Mathematics and Optimization – Springer Journals
Published: Apr 1, 2023
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