to be completely unrestricted for the corresponding model. The next table states the equations and systems of equations for Fourier transforms that follow from the convolution equations. Table 4. The form of the equations for the Fourier transforms: Table 3. Some nonparametric classes of generalized functions for which the convolution equations of the models are defined in S $^{∗}$. Model Sufficient assumptions 1 no restrictions: φ$_{x}$ ∗ ∈ ¯ C ; φ$_{u}$ ∈ ¯ C 2 no restrictions: φ$_{x}$ ∗ ∈ ¯ C ; φ$_{u}$ ∈ ¯ C Assumptions A Assumptions B 3 any φ$_{x}$ ∗ ∈ ¯ C ; φ$_{u}$ ∈ ¯ C (1) any φ$_{u}$ ∈ ¯ C ; φ$_{x}$ ∗ ∈ ¯ C (1) 4 any φ$_{u}$$_{x}$, φ$_{x}$ ∗ ∈ ¯ C ; φ$_{u}$ ∈ ¯ C (1) any φ$_{u}$, φ$_{x}$ ∗ ∈ ¯ C ; φ$_{u}$$_{x}$ ∈ ¯ C (1) 4a any φ$_{u}$$_{x}$, φ$_{x}$ ∗ ∈ ¯ C ; φ$_{u}$ ∈ ¯ C (1) any φ$_{u}$, φ$_{u}$$_{x}$ ∈ ¯ C ; φ$_{x}$ ∗ ∈ ¯ C (1) 5 any g ∈ S $^{∗}$; f$_{x}$ ∗ ∈ O$_{M}$ ; f$_{u}$ ∈ O ∗ C any f$_{x}$ ∗ ∈ ¯ D ; g, h$_{k}$ ∈ ¯ S B, $^{1}$; f$_{u}$ ∈ O ∗ C 6 any g ∈ S $^{∗}$; f$_{u}$ ∈ O ∗ C g ∈ O ∗ $_{C}$; any f$_{u}$ : φ$_{u}$ ∈ ¯ C 7 any g ∈ S $^{∗}$; f$_{u}$ ∈ O ∗ C g ∈ O ∗ $_{C}$; any f$_{u}$ : φ$_{u}$ ∈ ¯ C 35