TRANSFORMS ON WHITE-NOISE FUNCTIONALS WITH THEIR APPLICATIONS TO CAUCHY-PROBLEMS

A generalized Laplacian Delta(G)(K) is defined as a continuous linear operator acting on the space of test white noise functionals. Operator -parameter G(A,B)- and F-A,F-B-transforms on white noise functionals a re introduced and then prove a characterization theorem for G(A,B) and F-A,F-B-transforms in terms of the coordinate differential operator a nd the coordinate multiplication. As an application, we investigate th e existence and uniqueness of solution of the Cauchy problem for the h eat equation associated with Delta(G)(K).