ζ$_{0}$$_{ν}$. Then α$_{1}$ = β − 1 1 ε, and α$_{2}$, β$_{2}$ are defined as above by being 1 on ∪$_{v}$ W$_{v}$ and arbitrary outside of this set. The issue of the value of β at some point within each connected component arises. In the case of β being a character- istic function if there is only one connected component, W and 0 ∈ W the solution is unique, since then β (0) = 1 . 

Note that for model 5 the solution to equations of the type (8) would only provide F t ( gf$_{x}$ ∗ ) and φ$_{u}$ ; then from the first equation for this model in Table 4 φ$_{x}$ ∗ can be obtained; it is unique if supp φ$_{x}$ ∗ =supp φ$_{z}$ . To solve for g find g = F t − $^{1}$( F t ( gf$_{x}$ ∗ )) · ( f$_{x}$ ∗ ) − 1 . 

## 4 Identification, partial identification and well- posedness 

## 4.1 Identified solutions for the models 1-7 

As follows from the discussion of the solutions uniqueness in models 1,2,3,4,4a,5,6 holds (in a few cases up to a value of a function at a point) if all the Fourier transforms are supported over the whole R $^{d}$; in many cases it is sufficient that supp ( β, ∂ ) = R $^{d}$. 

The classes of functions could be defined with Fourier transforms sup- ported on some known subset ¯ W of R $^{d}$, rather than on the whole space; if all the functions considered have ¯ W as their support, and the support con- sists of one connected component that includes 0 as an interior point then 

