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defined on W by 

with the uniquely defined continuous functions κ$_{k}$ that solve 

or 

<img src='content_image/323668.jpg'>

<img src='content_image/323669.jpg'>

(b) if φ is continuously differentiable in W , φ (0) = 1 , then γ is uniquely defined on W by 

where 

with the uniquely defined on W continuous functions ˜ κ$_{k}$ that solve 

<img src='content_image/323671.jpg'>

<img src='content_image/323672.jpg'>

<img src='content_image/323670.jpg'>

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 

