with the uniquely defined continuous functions κ $_{k}$( ξ ) that solve or (b) φ is continuously differentiable in W , φ (0) = c κ $_{k}$( ξ ) ε$_{1}$ − iε$_{2}$$_{k}$ = 0 , k = 1 , ..., d ; where with the uniquely defined continuous functions κ $_{k}$( ξ ) that solve ε$_{1}$ ˜ $^{κ}$k − (( ε$_{1}$ ) ′ k − iε$_{2}$$_{k}$ ) = 0 , k = 1 , ..., d. ˜ φ ( ζ ) = exp ∫ ζ 0 Σ d k $_{=1}$˜ κ $_{k}$( ξ ) dξ$_{k}$, γ ( ζ ) = ˜ φ ( ζ ) − $^{1}$ε$_{i}$ ( ζ ) , (10) The proof is in proof of Theorem 3 and the Corollary of Zinde-Walsh, 2010. If support of φ coincides with support of γ, φ (and thus the function f ) is identified. The proof is set in the space S ′ of generalized functions and does not rely on existence of densities. The proof of (b) in the univariate case was first provided in Zinde-Walsh 2009, correcting the result of Schennach 2007. The formula for the density in Cunha et al. 2010 is valid in case (a) and can be interpreted in terms of generalized functions (”distributions”). In case 9