convoluting with a generalized δ − function is natural when considering the problems in spaces of generalized functions. 

The spaces of generalized functions most relevant for solving these prob- lems are the space S ′ (tempered distributions); space D ′ and some related spaces also play a role in the proofs. See e.g. Zinde-Walsh, 2010 for the definitions, discussion and summary of useful properties. 

The next section 2 presents the full solution to system of equations (6) extending all the results in the current literature. 

Section 3 discusses well-posedness. This is to clarify two issues: under what conditions consistent estimation of the identified general model is possi- ble and in what sense does a possibly mis-specified parametric model deliver valid analysis. The answer hinges on well-posedness of the identification of the function g. Well-posedness refers to g depending on the distributions of the observed variables in a continuous fashion. Well-posedness does not hold if both the function g and the density f are supersmooth (that is their Fourier transforms decline exponentially); on the other hand if any one of the two is such that the Fourier transform is continuously differentiable and its inverse is a regular generalized function (grows no faster than some power), then well-posedness in the weak topology of generalized functions obtains; for well-posedness in stronger topologies additional conditions need to be provided. An example shows that a Gaussian density for both functions would lead to violation of well-posedness. Classes of nonparametric models that include the Gaussian and that lead to a well-posed problem are defined. 

