satisfied for b = η − 1 well-posedness will hold. Example in Zinde-Walsh (2012) demonstrates that well-posedness of de- convolution will not hold even in the weak topology of S ∗ for super-smooth (e.g. Gaussian) distributions on unbounded support. On the other hand, well-posedness of deconvolution in S ∗ obtains for ordinary smooth distribu- tions and thus under less restrictive conditions than in function spaces, such as L$_{1}$ or L$_{2}$ usually considered. In the models 3-7 with several unknown functions, more conditions are required to ensure that all the operations by which the solutions are obtained are continuous in the topology of S $^{∗}$. It may not be sufficient to assume (1) for the inverses of unknown functions where the solution requires division; for continuity of the solution the condition may need to apply uniformly. Define a class of ordinary functions on R $^{d}$, Φ( m, V ) (with m a vector of integers, V a positive constant) where b ∈ Φ( m, V ) if Then in Zinde-Walsh (2012) well-posedness is proved for model 7 as long as in addition to Assumption A or B, for some Φ( m, V ) both φ$_{u}$ and φ − 1 u belong to the class Φ( m, V ). This condition is fulfilled by non-supersmooth φ$_{u}$ ; this could be an ordinary smooth distribution or a mixture with some mass point. A convenient way of imposing well-posedness is to restrict the support of 48 ∫ Π ( (1 + t 2 $_{i}$) − $^{1}$) m i | b ( t ) | dt < V < ∞ . (10)