in D $^{∗}$( S $^{∗}$) . Schennach (2007) considered univariate errors in variables model with instrumental variables and a regression function, g, bounded by polyno- mials; these regression functions are in S $^{∗}$, convolution with any generalized density function from O ∗ C exists in S $^{∗}$. For regression functions g in subspaces of S ∗ where growth is more restricted, convolution with less rapidly declining f may exist. For a generalized function g denote by h$_{k}$ the product of g by the k th component of x ∈ R $^{d}$, x$_{k}$ , for a regular function g ( x ) this is h$_{k}$ ( x ) = x$_{k}$g ( x ). In many cases when the convolution g ∗ f is defined, the convolution h$_{k}$ ∗ f is also defined. Indeed, this is so in all the examples above: if g has compact support, so does any h$_{k}$ ; if g ∈ C $^{∞}$, it is true of h$_{k}$ as well, etc. Thus some models accommodate not only (2), but also other equations, e.g. providing (3). 2.3 Fourier transforms, exchange formula and some special convolution pairs Next, consider the Fourier transforms and the exchange formula. For the generalized functions in equations (3) denote Fourier transforms as γ = F t ( g ) , φ = F t ( f ) and ε$_{i}$ = F t ( w$_{i}$ ) . Recall that the Fourier transform always exists in S ∗ and is a continuous isomorphism. 21 Assumption 3. The statistical model is such that in addition to Assump- tion 2, h$_{k}$ ∈ A , k = 1 , ..., d.