of some order of a continuous function; to be an element of S ∗ such a con- tinuos function cannot grow faster than a polynomial. More specifically, by Schwartz (1966, theorem VI, p.239) any generalized function from b ∈ S ∗ can be represented as a generalized derivative of a continuous function: b = ∂ $^{l}$c for a continuous function c ( x ) , which can be written as c ( x ) = (1 + x $^{2}$) m 2 ˜ c ( x ) , where the continuous function ˜ c ( x ) is uniformly bounded on R $^{d}$: | ˜ c | < V. Consider some fixed vectors of non-negative integers, l and m and a bound V. Denote by S ∗ $_{l,m}$( V ) the class of generalized functions, b, that have such a representation for l , m and continuous ˜ c : | ˜ c ( x ) | < V ; any bounded in the topology of S ∗ set of generalized functions has the representation S ∗ $_{l,m}$( V ) (see Schwartz, 1966, (VII,5;5), p.246-247). The smallest such l is the order of integration that applied to a generalized function produces a continuous function and is related to the degree of singularity of the generalized function, while m characterizes its growth at infinity. The Fourier transform ( Ft ) is defined for functions in D, and more gen- erally in S ; it is an isomorphism of the space S ; the value of the Fourier transform for the test function ψ ∈ S also belongs to S and its value at any s ∈ R d is Ft ( ψ )( s ) = ∫ ψ ( x ) e ix $^{$^{T}$s}$dx ( x T denotes transpose); in the dual spaces D ∗ and S ∗ the Fourier transform is given by ( Ft ( b ) , ψ ) = ( b, Ft ( ψ )). The Fourier transform is an isomorphism of the space S $^{∗}$. For the analysis of this paper we mostly consider the functions of inter- est in the generalized functions space S $^{∗}$, because of the fact that Fourier transform represents an isomorphism which permits to apply it or its inverse 17