defined on W by with the uniquely defined continuous functions κ$_{k}$ that solve or (b) if φ is continuously differentiable in W , φ (0) = 1 , then γ is uniquely defined on W by γ ( s ) = c exp ∫ s 0 ∑ d k $_{=1}$κ$_{k}$ ( t ) dt$_{k}$, (17) κ$_{k}$ ε$_{1}$ − iε$_{2}$$_{k}$ = 0 , k = 1 , ..., d ; γ = ˜ φ − $^{1}$ε$_{1}$ , (18) ˜ φ ( s ) = exp ∫ s 0 ∑ d k $_{=1}$˜ κ$_{k}$ ( t ) dt$_{k}$, ε$_{1}$ ˜ κ$_{k}$ − (( ε$_{1}$ ) ′ k − iε$_{2}$$_{k}$ ) = 0 , k = 1 , ..., d. with the uniquely defined on W continuous functions ˜ κ$_{k}$ that solve Then g = F t − $^{1}$( γ ) . If supp( γ ) = W, then g is uniquely defined. Uniqueness holds automatically if W = R $^{d}$. If supp( φ ) = W, then φ is also uniquely defined; and so is f = F t − $^{1}$( φ ) . Proof. (a) Consider the space of generalized functions D $^{∗}$( W ) (defined in proof of Lemma 1). Since continuous γ is non-zero on W by Lemma 1 (reversing the roles of φ and γ there) in D $^{∗}$( W ) the generalized function 30 where