@article{Gerasimenko_Shtyk_2006, title={Initial-value problem for the Bogolyubov hierarchy for quantum systems of particles}, volume={58}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3521}, abstractNote={We construct cumulant (semi-invariant) representations for a solution of the initial-value problem for the Bogolyubov hierarchy for quantum systems of particles. In the space of sequences of trace-class operators, we prove a theorem on the existence and uniqueness of a solution. We study the equivalence problem for various representations of a solution in the case of the Maxwell-Boltzmann statistics.}, number={9}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Gerasimenko, V. I. and Shtyk, V. O.}, year={2006}, month={Sep.}, pages={1175–1191} }