On virial expansions of correlation functions. Canonical ensemble - Pogorelov, Yu.; Rebenko, A. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 517.9 We present a survey of works of the Kyiv School of Mathematicians published in Soviet journals in the 1940–70s. The main results are presented in the language of contemporary methods of infinite-dimensional analysis, which significantly simplifies their proofs. Nonlinear (in the density parameter) Kirkwood–Salzburg-type equations are obtained for the correlation functions of canonical ensemble. The existence and uniqueness of solution is established under the conditions of high temperature and low density. The material presented in our survey is supplemented by the original research of one of the authors [A. L. Rebenko, Virial expansions for correlation functions in canonical ensemble, Preprint arXiv:2205.07095 [math-ph], https://doi.org/10.48550/arXiv.2205.07095] in which new expansions in the density parameter are constructed for the correlation functions.