Geodesic
The application of a convolution transform to the theory of the generalized Stieltjes moment problem
Izvestiya. Mathematics , Tome 1 (1967) no. 3, pp. 475-514

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In this article we present a new method of studying the generalized Stieltjes moment problem that is connected with the application of convolution transforms. Using this method, we consider the existence and uniqueness of solutions to the problem and we prove a number of new results. Moreover, the question of uniqueness is considered under less restrictive conditions than in other investigations. 
@article{IM2_1967_1_3_a0,
     author = {G. V. Badalyan},
     title = {The application of a convolution transform to the theory of the generalized {Stieltjes} moment problem},
     journal = {Izvestiya. Mathematics },
     pages = {475--514},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {1967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_3_a0/}
}
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G. V. Badalyan. The application of a convolution transform to the theory of the generalized Stieltjes moment problem. Izvestiya. Mathematics , Tome 1 (1967) no. 3, pp. 475-514. http://geodesic.mathdoc.fr/item/IM2_1967_1_3_a0/