Interpolation and absolutely convergent series in Frechet spaces

A theorem due to Eidelheit concerning the interpolation problem for a sequence of continuous linear functionals in a Frechet space is generalized. A solvability criterion for the interpolation problem is obtained in the form of an absolutely convergent series whose elements are in a fixed set. A solution of the system of equations for a sequence of functionals is constructed explicitly in a particular case. These results are then applied to spaces of holomorphic functions.