Open Access

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

### 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.

Key words: Projection spectral theorem, Kondratiev--Kuna convolution, Lenard transform, Bogolyubov functional

### Article Information

 Title The investigation of Bogoliubov functionals by operator methods of moment problem Source Methods Funct. Anal. Topology, Vol. 22 (2016), no. 1, 1-47 MathSciNet MR3522860 zbMATH 06630281 Milestones Received 21/04/2011; Revised 03/08/2015 Copyright The Author(s) 2016 (CC BY-SA)

### Authors Information

Yu. M. Berezansky
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

V. A. Tesko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

Yu. M. Berezansky and V. A. Tesko, The investigation of Bogoliubov functionals by operator methods of moment problem, Methods Funct. Anal. Topology 22 (2016), no. 1, 1-47.

### BibTex

@article {MFAT593,
AUTHOR = {Berezansky, Yu. M. and Tesko, V. A.},
TITLE = {The investigation of Bogoliubov functionals by operator methods of moment problem},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {22},
YEAR = {2016},
NUMBER = {1},
PAGES = {1-47},
ISSN = {1029-3531},
MRNUMBER = {MR3522860},
ZBLNUMBER = {06630281},
URL = {http://mfat.imath.kiev.ua/article/?id=593},
}

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