# 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 (ESCI), Google Scholar.

## Latest Articles (September, 2016)

### Fractional statistical dynamics and fractional kinetics

José Luís da Silva, Anatoly N. Kochubei, Yuri Kondratiev

Methods Funct. Anal. Topology **22** (2016), no. 3, 197-209

We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum in terms of solutions to Vlasov-type hierarchies. As a by-product we obtain the evolution of the density of particles in the fractional kinetics in terms of a non-linear Vlasov-type kinetic equation. As an application we study the intermittency of the fractional mesoscopic dynamics.

### Some results on order bounded almost weak Dunford-Pettis operators

Nabil Machrafi, Aziz Elbour, Mohammed Moussa

Methods Funct. Anal. Topology **22** (2016), no. 3, 256-265

We give some new characterizations of almost weak Dunford-Pettis operators and we investigate their relationship with weak Dunford-Pettis operators.

### Homeotopy groups of rooted tree like non-singular foliations on the plane

Methods Funct. Anal. Topology **22** (2016), no. 3, 283-294

Let $F$ be a non-singular foliation on the plane with all leaves being closed subsets, $H^{+}(F)$ be the group of homeomorphisms of the plane which maps leaves onto leaves endowed with compact open topology, and $H^{+}_{0}(F)$ be the identity path component of $H^{+}(F)$. The quotient $\pi_0 H^{+}(F) = H^{+}(F)/H^{+}_{0}(F)$ is an analogue of a mapping class group for foliated homeomorphisms. We will describe the algebraic structure of $\pi_0 H^{+}(F)$ under an assumption that the corresponding space of leaves of $F$ has a structure similar to a rooted tree of finite diameter.

### Non-autonomous interacting particle systems in continuum

Methods Funct. Anal. Topology **22** (2016), no. 3, 220-244

A conservative Feller evolution on continuous bounded functions is constructed from a weakly continuous, time-inhomogeneous transition function describing a pure jump process on a locally compact Polish space. The transition function is assumed to satisfy a Foster-Lyapunov type condition. The results are applied to interacting particle systems in continuum, in particular to general birth-and-death processes (including jumps). Particular examples such as the BDLP and Dieckmann-Law model are considered in the end.