Geodesic
The Stieltjes Moment Problem
Canadian mathematical bulletin, Tome 24 (1981) no. 3, pp. 279-282

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We shall apply the spectral theorem for self adjoint operators in Hilbert space to study an operator version of the Stieltjes moment problem [1]. In the course of the work we shall make use of the Friedrichs extension theorem which states that any non-negative symmetric operator in Hilbert space has a non-negative self adjoint extension. 
Klambauer, G. The Stieltjes Moment Problem. Canadian mathematical bulletin, Tome 24 (1981) no. 3, pp. 279-282. doi: 10.4153/CMB-1981-044-6
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     author = {Klambauer, G.},
     title = {The {Stieltjes} {Moment} {Problem}},
     journal = {Canadian mathematical bulletin},
     pages = {279--282},
     year = {1981},
     volume = {24},
     number = {3},
     doi = {10.4153/CMB-1981-044-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1981-044-6/}
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