Geodesic
The moments problem for rapidly decreasing functions
Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 66-74.

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Function classes are described in which the moments problem $$ \int_0^{+\infty}t^{\alpha_n}f(t)dt=c_n $$ is solvable for any right-hand sides from a sequence $\{c_n\}$. Constructive solutions are given. The results obtained generalize and supplement some theorems proved earlier by other mathematicians. 
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     author = {A. Yu. Popov},
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A. Yu. Popov. The moments problem for rapidly decreasing functions. Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 66-74. http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a6/

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