content_image/316810.jpg content_image/316808.jpg
The continuity assumption on the characteristic function is typically made; any characteristic function satisfies(7) . 

By Theorem 1 of Zinde-Walsh 2010 then the following system of equations holds in S $^{′}$. 

<img src='content_image/316810.jpg'>

Assumption 3 . supp( φ ) ⊇ supp( γ ) = W, where W is a convex set in R d that includes an interior point 0 . 

The support assumption is necessary to solve for γ. The interior point in the case of characteristic functions is zero with the value of the continuous characteristic function equal to 1 at that point. If the system of equations involves functions with W having an interior point a ̸ = 0 consider shifted functions. 

## Theorem 1 Under Assumptions 1-3 if 

(a) γ is continuously differentiable in W, γ (0) = c 

<img src='content_image/316808.jpg'>

