The functions ε are Fourier transforms of the corresponding w, and ε$_{k}$ = − iF t ( w$_{k}$ ) defined for the models in Tables 1 and 2. Assumption 2 (that is fulfilled e.g. by generalized functions classes of 36 Model Eq’s for Fourier transforms Unknown functions 1 φ$_{x}$ ∗ φ$_{u}$ = φ$_{z}$ ; φ$_{x}$ ∗ 2 φ$_{x}$ ∗ = φ$_{z}$φ$_{−}$$_{u}$ ; φ$_{x}$ ∗ 3     φ$_{x}$ ∗ φ$_{u}$ = φ$_{z}$ ; ( φ$_{x}$ ∗ ) ′ k φ$_{u}$ = ε$_{k}$, k = 1 , ..., d. φ$_{x}$ ∗ , φ$_{u}$ 4      φ$_{x}$ ∗ φ$_{u}$ = φ$_{z}$ ; ( φ$_{x}$ ∗ ) ′ k φ$_{u}$ = ε$_{k}$, k = 1 , ..., d ; φ$_{x}$ ∗ φ$_{u}$$_{x}$ = φ$_{x}$. φ$_{x}$ ∗ , φ$_{u}$, φ$_{u}$$_{x}$ 4a      φ$_{u}$$_{x}$φ$_{u}$ = φ$_{z}$$_{−}$$_{x}$ ; ( φ$_{u}$$_{x}$ ) ′ k φ$_{u}$ = ε$_{k}$, k = 1 , ..., d. φ$_{x}$ ∗ φ$_{u}$$_{x}$ = φ$_{x}$. –”– 5      φ$_{x}$ ∗ φ$_{u}$ = φ$_{z}$ ; F t ( gf$_{x}$ ∗ ) φ$_{u}$ = ε ( F t ( gf$_{x}$ ∗ )) ′ k φ$_{u}$ = ε$_{k}$, k = 1 , ..., d. φ$_{x}$ ∗ , φ$_{u}$, g 6     φ$_{x}$ = φ$_{−}$$_{u}$φ$_{z}$ ; F t ( g ) φ$_{−}$$_{u}$ = ε. φ$_{u}$, g 7    F t ( g ) φ$_{u}$ = ε ; ( F t ( g )) ′ k φ$_{u}$ = ε$_{k}$, k = 1 , ..., d. φ$_{u}$, g  k Notes. Notation ( · ) ′ k denotes the k-th partial derivative of the function.