Interpolation and absolutely convergent series in Fréchet spaces. (January 2019) - Merzlyakov, S. G.
Abstract: A theorem due to Eidelheit concerning the interpolation problem for a sequence of continuous linear functionals in a Fréchet 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. Bibliography: 15 titles.