# The investigation of Bogoliubov functionals by operator methods of moment problem

#### Yu. M. Berezansky, V. A. Tesko

Methods Funct. Anal. Topology **22** (2016), no. 1, 1-47

## Abstract

The article is devoted to a study of Bogoliubov functionals by using methods of the operator spectral theory being applied to the classical power moment problem. Some results, similar to corresponding ones for the moment problem, where obtained for such functionals. In particular, the following question was studied: under what conditions a sequence of nonlinear functionals is a sequence of Bogoliubov functionals.