Geodesic
Inclusion of Hamburger's power moment problem in the spectral theory of the canonical systems
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 147-171

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Hamburger's power moment problem (shortly HPMP) that has a solution with infinitely many points of increase is shown to be the problem of finding all spectral functions for some canonical system of the linear differential equations of phase dimension 2 and with Hamiltonian of special class. A rule for construction of this Hamiltonian using the data of HPMP is given. In this connection the Hamburger criterion for the uniqueness of a solution of HPMP acquires a “natural form”, and some results of the classical HPMP theory receive simple proofs. 
@article{ZNSL_1999_262_a6,
     author = {I. S. Kats},
     title = {Inclusion of {Hamburger's} power moment problem in the spectral theory of the canonical systems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {147--171},
     publisher = {mathdoc},
     volume = {262},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a6/}
}
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I. S. Kats. Inclusion of Hamburger's power moment problem in the spectral theory of the canonical systems. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 147-171. http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a6/