Thus for this ψ the values of the functional, ( γ$_{n}$ − γ, ψ ) diverge as n → ∞ , and so γ$_{n}$ − γ does not converge to zero in S $^{∗}$. ■ Note that since any ψ ∈ D has bounded support in the example conver- gence of γ$_{n}$ to γ holds in D $^{∗}$. 3.3 Well-posedness in S ∗ of the solution to the system of equations (16) Recall (13) and define a subclass of functions in S $^{∗}$, Φ( m, V ) , where b ∈ Φ( m, V ) if b satisfies the condition The requirement that b belong to Φ( m, V ) implies that (13) applies uni- formly in this class and also defines a bounded set in S $^{∗}$. The next Theorem considers well-posedness of the problem in (3) (and correspondingly, (16)) under the identification conditions of Theorem 3(b). The conditions of The- orem 3(a) can be similarly considered. ((1 + t $^{2}$) − $^{1}$) $^{m}$| b ( t ) | < V < ∞ (21) Theorem 5 Suppose that ( γ$_{n}$, φ$_{n}$ ) , n = 1 , 2 , ... and ( γ, φ ) belong to a product pair (Γ , Φ) . Additionally, let the conditions of Theorem 3(b) apply to each pair ( γ$_{n}$, φ$_{n}$ ) . Suppose that ε$_{1}$$_{n}$ − ε$_{1}$ → 0 and ε$_{2}$$_{kn}$ − ε$_{2}$$_{k}$ → 0 in S $^{∗}$; the functions φ, φ$_{n}$ as well as φ − $^{1}$, φ − 1 n restricted to W all belong to some Φ( m, V ) Then if (a) (Γ , Φ) ≡ ( S $^{∗}$, O$_{M}$ ) , or 41