content_image/311173.jpg content_image/311180.jpg
or to the system of equations 

<img src='content_image/311173.jpg'>

## 3 Solutions to the convolution equations: iden- tification and well-posedness 

## 3.1 Identification 

For identification the supports of the functions in the equations play an important role. 

Recall that for a continuous function ψ ( x ) on R d support is defined as the set W =supp( ψ ) , such that 

Support of a continuous function is an open set. 

<img src='content_image/311180.jpg'>

Since generalized functions can be considered as functionals on the space S support of a generalized function b ∈ S ∗ is defined as follows (Schwartz, 1966, p. 28). Denote by ( b, ψ ) the value of the functional b for ψ ∈ S. Consider open sets W with the property that for any ψ ∈ S : supp( ψ ) = W the value of the functional ( b, ψ ) = 0; then define the null set for b as the union 

