TY - JOUR AU - V. I. Gerasimenko AU - V. O. Shtyk PY - 2006/09/25 Y2 - 2024/03/29 TI - Initial-value problem for the Bogolyubov hierarchy for quantum systems of particles JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 58 IS - 9 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/3521 AB - 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. ER -