S ; the value of this functional for ψ ∈ S is denoted by ( b, ψ ) . When b is an ordinary (point-wise defined) real-valued function, such as a density of an absolutely continuous distribution or a regression function, the value of the functional on real-valued ψ defines it and is given by If b is a characteristic function it may be complex-valued, then the value of the functional b applied to ψ ∈ S where S is the space of complex-valued functions, is where overbar denotes complex conjugate. The integrals are taken over the whole space R $^{d}$. The generalized functions in the space S ∗ are continuously differentiable and the differentiation operator is continuous; Fourier transforms and their inverses are defined for all b ∈ S $^{∗}$, the operator is a (continuos) isomorphism of the space S $^{∗}$. However, convolutions and products are not defined for all pairs of elements of S $^{∗}$, unlike, say, the space L$_{1}$ ; on the other hand, in L$_{1}$ differentiation is not defined and not every distribution has a density that is an element of L$_{1}$. Assumption 1 places no restrictions on the distributions, since in S ∗ any distribution function is differentiable and the differentiation operator is con- tinuous. The advantage of not restricting distributions to be absolutely con- 10 ( b, ψ ) = ∫ b ( x ) ψ ( x ) dx. ( b, ψ ) = ∫ b ( x ) ψ ( x ) dx,