  This paper provides a nonparametric analysis for several classes of models,
with cases such as classical measurement error, regression with errors in
variables, factor models and other models that may be represented in a form
involving convolution equations. The focus here is on conditions for existence
of solutions, nonparametric identification and well-posedness in the space of
generalized functions (tempered distributions). This space provides advantages
over working in function spaces by relaxing assumptions and extending the
results to include a wider variety of models, for example by not requiring
existence of density. Classes of (generalized) functions for which solutions
exist are defined; identification conditions, partial identification and its
implications are discussed. Conditions for well-posedness are given and the
related issues of plug-in estimation and regularization are examined.
