We consider a family B of self-adjoint commuting operators b ς = ∫ ς(t) dB t where B t is a quantum compound Poisson process in a Fock space. By using the projection spectral theorem, we construct the Fourier transform in generalized joint eigenvectors of the family B which is unitary between the Fock space and the L 2-space of compound Poisson white noise, (L 2CP). This construction gives the possibility of introducing spaces of test and generalized functions the dual pairing of which is determined by the inner product of (L 2 CP)