or to the system of equations γ · φ = ε$_{1}$ (16) γ ′ k · φ = iε$_{2}$$_{k}$, k = 1 , ..., d. 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. 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 ψ ( x ) =     a = 0 for x ∈ W 0 for x ∈ R $^{d}$\ W. 26