generalized function b ∈ S ∗ is defined as follows (Schwartz, 1967, p. 28). Denote by ( b, ψ ) the value of the functional b for ψ ∈ S. Define a null set for b ∈ S ∗ as the union of supports of all functions in S for which the value of the functional is zero: Ω = {∪ supp( ψ ) , ψ ∈ S, such that ( b, ψ ) = 0 } . Then supp( b ) = R $^{d}$\ Ω . Note that a generalized function has support in a closed set, for example, support of the δ − f unction is just one point 0. Note that for model 2 Table 4 gives the solution for φ$_{x}$ ∗ directly and the inverse Fourier transform can provide the (generalized) density function, f$_{x}$ ∗ . In Zinde-Walsh (2012) identification conditions in S ∗ were given for mod- els 1 and 7 under assumptions that include the ones in Table 3 but could also be more flexible. The equations in Table 3 for models 1,3, 4, 4a, 5, 6 and 7 are of two types, similar to those solved in Zinde-Walsh (2012). One is a convolution with one unknown function; the other is a system of equations with two unknown functions, each leading to the corresponding equations for their Fourier transforms. Consider the equation with one unknown function α ; β is a given continuous function. By assump- tion 2 the non-parametric class for α is such that the equation holds in S ∗ on 38 αβ = γ, (5) 3.2.1 Solutions to the equation αβ = γ.