Geodesic
Construction of solutions of Toda lattices by the classical moment problem
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 113-129

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Making use of formulas of J. Moser for a finite-dimensional Toda lattices, we derive the evolution law for moments of the spectral measure of the semi-infinite Jacobi operator associated with the nonlinear system. This allows us to construct solutions of semi-infinite Toda lattices for a wide class of unbounded initial data by using well-known results from the classical moment problem theory. 
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     author = {A. S. Mikhailov and V. S. Mikhailov},
     title = {Construction of solutions of {Toda} lattices by the classical moment problem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--129},
     publisher = {mathdoc},
     volume = {506},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a10/}
}
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A. S. Mikhailov; V. S. Mikhailov. Construction of solutions of Toda lattices by the classical moment problem. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 51, Tome 506 (2021), pp. 113-129. http://geodesic.mathdoc.fr/item/ZNSL_2021_506_a10/