Siberian Federal University

To each analytic functional on the space O′ (Cn), a function f(z) holomorphic in a neighbor- hood of the origin and an entire function of exponential type F(z) are associated so that the coefficients c of the power series expansion of f(z) are given by values of F( ). We study the problem of finding a connection between the domain where the function f(z) extends to and the growth of the function F(z)