Geodesic
The moments problem for rapidly decreasing functions
Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 66-74 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@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/}
}
TY  - JOUR
AU  - A. Yu. Popov
TI  - The moments problem for rapidly decreasing functions
JO  - Matematičeskie zametki
PY  - 1996
SP  - 66
EP  - 74
VL  - 60
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a6/
LA  - ru
ID  - MZM_1996_60_1_a6
ER  - 
%0 Journal Article
%A A. Yu. Popov
%T The moments problem for rapidly decreasing functions
%J Matematičeskie zametki
%D 1996
%P 66-74
%V 60
%N 1
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a6/
%G ru
%F MZM_1996_60_1_a6
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/

[1] Polya G., “Sur l'indetermination d'un problème voisin du problème des moments”, C. R. Acad. Sci. Paris, 207 (1938), 708–711 | MR | Zbl

[2] Duran A. J., “The Stieltjes moments problem for rapidly decreasing functions”, Proc. Amer. Math. Soc., 107 (1989), 731–741 | DOI | MR | Zbl

[3] Markushevich A. I., Teoriya analiticheskikh funktsii, T. 2, Nauka, M., 1968

[4] Titchmarsh E., Teoriya funktsii, GITTL, M.–L., 1951

[5] Kazmin Yu. A., “Ob odnoi zadache A. O. Gelfonda”, Matem. sb., 90 (132):4 (1973), 521–543 | MR | Zbl