Geodesic
Topological structure of~the family of~solutions of~the Bogolyubov equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 2, pp. 243-252

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The Bogoliubov equation for generating functionals of classical statistical physics is studied in a specially constructed Banach space $H_\alpha$ of analytic functionals. Properties of closedness, compactness and convexity of the family of solutions of this equation in various topologies of the space $H_\alpha$ are considered. On the basis of the results obtained, the problem of the transition to the thermodynamic limit in the generating functional method is solved. 
@article{TMF_1980_42_2_a8,
     author = {G. I. Nazin},
     title = {Topological structure of~the family of~solutions of~the {Bogolyubov} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {243--252},
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {1980},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a8/}
}
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G. I. Nazin. Topological structure of~the family of~solutions of~the Bogolyubov equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 42 (1980) no. 2, pp. 243-252. http://geodesic.mathdoc.fr/item/TMF_1980_42_2_a8/