# Methods of Functional Analysis

and Topology

Editors-in-Chief: Yu. M. Berezansky,
Yu. G. Kondratiev

ISSN: 1029-3531 (Print) 2415-7503 (Online)

Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed, open access journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.

MFAT is indexed in: MathSciNet, zbMATH, Google Scholar.

## Latest Articles (March, 2016)

### Dynamical systems of conflict in terms of structural measures

Volodymyr Koshmanenko, Inga Verygina

Methods Funct. Anal. Topology **22** (2016), no. 1, 81-93

We investigate the dynamical systems modeling conflict processes between a pair of opponents. We assume that opponents are given on a common space by distributions (probability measures) having the similar or self-similar structure. Our main result states the existence of the controlled conflict in which one of the opponents occupies almost whole conflicting space. Besides, we compare conflicting effects stipulated by the rough structural approximation under controlled redistributions of starting measures.

### 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

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.

### On a generalization of the three spectral inverse problem

O. P. Boyko, O. M. Martynyuk, V. N. Pivovarchik

Methods Funct. Anal. Topology **22** (2016), no. 1, 74-80

We consider a generalization of the three spectral inverse problem, that is, for given spectrum of the Dirichlet-Dirichlet problem (the Sturm-Liouville problem with Dirichlet conditions at both ends) on the whole interval $[0,a]$, parts of spectra of the Dirichlet-Neumann and Dirichlet-Dirichlet problems on $[0,a/2]$ and parts of spectra of the Dirichlet-Newman and Dirichlet-Dirichlet problems on $[a/2,a]$, we find the potential of the Sturm-Liouville equation.

### Joint functional calculus in algebra of polynomial tempered distributions

Methods Funct. Anal. Topology **22** (2016), no. 1, 62-73

In this paper we develop a functional calculus for a countable system of generators of contraction strongly continuous semigroups. As a symbol class of such calculus we use the algebra of polynomial tempered distributions. We prove a differential property of constructed calculus and describe its image with the help of the commutant of polynomial shift semigroup. As an application, we consider a function of countable set of second derivative operators.