Geodesic
The moment problem, interpolation and basicity
Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 277-306

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The article contains criteria for the solvability of the general moment problem in countably Hilbert spaces. The relationship between the general interpolation problem in reflexive spaces and the corresponding moment problem is also established. The results lead on the one hand to criteria for solvability of the general interpolation problem (and, in particular, of the Hermite problem) in various function spaces, and, on the other hand, to necessary and sufficient conditions for a system $\{z^{p_k}f(\lambda_kz)\}$, where $f$ is an entire function, to form a basis in its linear hull. Bibliography: 27 titles. 
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     author = {Yu. F. Korobeinik},
     title = {The moment problem, interpolation and basicity},
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     year = {1979},
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Yu. F. Korobeinik. The moment problem, interpolation and basicity. Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 277-306. http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a4/