  We study the possibility to reconstruct the primordial function for some
periodic function. The procedure includes an analytical continuation of a
discrete function for Fourier coefficients computation, that introduces an
ambiguity. To establish conditions under which no ambiguity appears, the
modification of Carlson theorem is suggested. In a case when no subsidiary
condition is imposed, ambiguity in the definition of primordial function does
not go beyond the functions which belong to space $\Omega^{\prime}$.
