Geodesic
Convergence of the virial expansion for the classical canonical ensemble
Teoretičeskaâ i matematičeskaâ fizika, Tome 24 (1975) no. 2, pp. 248-254 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Yu. G. Pogorelov},
     title = {Convergence of the virial expansion for the classical canonical ensemble},
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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/

[1] D. Ryuel, Statisticheskaya mekhanika (strogie rezultaty), «Mir», 1972

[2] N. N. Bogolyubov, B. I. Khatset, DAN SSSR, 66 (1949), 321 | MR | Zbl

[3] N. N. Bogolyubov, D. Ya. Petrina, B. I. Khatset, TMF, 1 (1969), 251

[4] N. N. Bogolyubov, Problemy dinamicheskoi teorii v statisticheskoi fizike, Gostekhizdat, 1946 | MR

[5] R. Edvards, Funktsionalnyi analiz (teoriya i prilozheniya), «Mir», 1969