Geodesic
Convergence of the virial expansion for the classical canonical ensemble
Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 248-254

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The infinite set of coupled integral equations for correlation functions in the case of classical canonical ensemble similar to those of Kirkwood–Salsburg is derived starting with the Bogoliubov integral-differential equations. The theorem of existence and uniqueness of solution is proved for such equations by the method of a non-linear operator ones in the Banach space. The solution has a form of the power series in density. 
@article{TMF_1975_24_2_a11,
     author = {Yu. G. Pogorelov},
     title = {Convergence of the virial expansion for the classical canonical ensemble},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {248--254},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a11/}
}
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Yu. G. Pogorelov. Convergence of the virial expansion for the classical canonical ensemble. Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 248-254. http://geodesic.mathdoc.fr/item/TMF_1975_24_2_a11/