  In this paper we consider interpolation problem connected with series by
integer shifts of Gaussians. Known approaches for these problems met numerical
difficulties. Due to it another method is considered based on finite-rank
approximations by linear systems. The main result for this approach is to
establish correctness of the finite-rank linear system under consideration. And
the main result of the paper is to prove correctness of the finite-rank linear
system approximation. For that an explicit formula for the main determinant of
the linear system is derived to demonstrate that it is non-zero.
