Geodesic
The moments problem for rapidly decreasing functions
Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 66-74 
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/
@article{MZM_1996_60_1_a6,
     author = {A. Yu. Popov},
     title = {The moments problem for rapidly decreasing functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {66--74},
     year = {1996},
     volume = {60},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a6/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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