Geodesic
Interpolation and absolutely convergent series in Fr\'echet spaces
Sbornik. Mathematics, Tome 210 (2019) no. 1, pp. 105-144

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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.
Keywords: absolutely convergent series, continuous linear functionals, spaces of holomorphic functions, series of exponentials.
Mots-clés : Fréchet space, interpolation 
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     author = {S. G. Merzlyakov},
     title = {Interpolation and absolutely convergent series in {Fr\'echet} spaces},
     journal = {Sbornik. Mathematics},
     pages = {105--144},
     publisher = {mathdoc},
     volume = {210},
     number = {1},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_1_a3/}
}
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S. G. Merzlyakov. Interpolation and absolutely convergent series in Fr\'echet spaces. Sbornik. Mathematics, Tome 210 (2019) no. 1, pp. 105-144. http://geodesic.mathdoc.fr/item/SM_2019_210_1_a3/