  This is a companion note to Zinde-Walsh (2010), arXiv:1009.4217v1[MATH.ST],
to clarify and extend results on identification in a number of problems that
lead to a system of convolution equations. Examples include identification of
the distribution of mismeasured variables, of a nonparametric regression
function under Berkson type measurement error, some nonparametric panel data
models, etc. The reason that identification in different problems can be
considered in one approach is that they lead to the same system of convolution
equations; moreover the solution can be given under more general assumptions
than those usually considered, by examining these equations in spaces of
generalized functions. An important issue that did not receive sufficient
attention is that of well-posedness. This note gives conditions under which
well-posedness obtains, an example that demonstrates that when well-posedness
does not hold functions that are far apart can give rise to observable
arbitrarily close functions and discusses misspecification and estimation from
the stand-point of well-posedness.
