# 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 arXiv overlay 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 an open access journal, free for authors and free for readers.

MFAT is indexed in: MathSciNet, zbMATH, Web of Science, DOAJ, Google Scholar.

## Latest Articles (June, 2017)

### Initial-boundary value problems for two-dimensional parabolic equations in Hörmander spaces

Methods Funct. Anal. Topology **23** (2017), no. 2, 177-191

We investigate a general nonhomogeneous initial-boundary value problem for a two-dimensional parabolic equation in some anisotropic Hörmander inner product spaces. We prove that the operators corresponding to this problem are isomorphisms between appropriate Hörmander spaces.

### Asymptotic properties of the $p$-adic fractional integration operator

Anatoly N. Kochubei, Daniel S. Soskin

Methods Funct. Anal. Topology **23** (2017), no. 2, 155-163

We study asymptotic properties of the $p$-adic version of a fractional integration operator introduced in the paper by A. N. Kochubei, Radial solutions of non-Archimedean pseudo-differential equations, Pacif. J. Math. 269 (2014), 355-369.

### Evolution of correlation operators of large particle quantum systems

Methods Funct. Anal. Topology **23** (2017), no. 2, 123-132

The paper deals with the problem of a rigorous description of the evolution of states of large particle quantum systems in terms of correlation operators. A nonperturbative solution to a Cauchy problem of a hierarchy of nonlinear evolution equations for a sequence of marginal correlation operators is constructed. Moreover, in the case where the initial states are specified by a one-particle density operator, the mean field scaling asymptotic behavior of the constructed marginal correlation operators is considered.

### Fixed points of complex systems with attractive interaction

Methods Funct. Anal. Topology **23** (2017), no. 2, 164-176

We study the behavior of complex dynamical systems describing an attractive interaction between two opponents. We use the stochastic interpretation and describe states of systems in terms of probability distributions (measures) and their densities. For the time evolution we derive specific non-linear difference equations which generalize the well-known Lotka-Volterra equations. Our results state the existence of fixed points (equilibrium states) for various kinds of attractive interactions. Besides, we present an explicit description of the limiting distributions and illustrate abstract results by several examples.