# 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)

### On universal coordinate transform in kinematic changeable sets

Methods Funct. Anal. Topology **23** (2017), no. 2, 133-154

This work is devoted to a study of abstract coordinate transforms in kinematic changeable sets. Investigations in this direction may be interesting for astrophysics, because there exists a hypothesis that, in a large scale of the Universe, physical laws (in particular, the laws of kinematics) may be different from the laws acting in a neighborhood of our solar System.

### On behavior at infinity of solutions of elliptic differential equations in a Banach space

M. L. Gorbachuk, V. M. Gorbachuk

Methods Funct. Anal. Topology **23** (2017), no. 2, 108-122

For a differential equation of the form $y''(t) - By(t) = 0, \ t \in (0, \infty)$, where $B$ is a weakly positive linear operator in a Banach space $\mathfrak{B}$, the conditions on the operator $B$, under which this equation is uniformly or uniformly exponentially stable are given. As distinguished from earlier works dealing only with continuous at 0 solutions, in this paper no conditions on behavior of a solution near 0 are imposed.

### 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.

### 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.