Abstract

• We are interested in quadratic white noise functionals. First we define the two subspaces H2(-2,1) and H2(-2,2) of the space of quadratic functionals of white noise. By introducing a random measure dz(ɷ), we consider a Hilbert space spanned by {ƪ f (u) d (u) z }. Then we can see the duality between the two spaces H2(-2,1) and H2(-2,2) In addition, when we consider the Lévy Laplacian on H2(-2,1) we can obtain the adjoint of the Lévy Laplacian on H2(-2,2)