# 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 (December, 2016)

### L-Dunford-Pettis property in Banach spaces

Methods Funct. Anal. Topology **22** (2016), no. 4, 387-392

In this paper, we introduce and study the concept of L-Dunford-Pettis sets and L-Dunford-Pettis property in Banach spaces. Next, we give a characterization of the L-Dunford-Pettis property with respect to some well-known geometric properties of Banach spaces. Finally, some complementability of operators on Banach spaces with the L-Dunford-Pettis property are also investigated.

### Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum

Martin Friesen, Oleksandr Kutoviy

Methods Funct. Anal. Topology **22** (2016), no. 4, 346-374

Two coupled spatial birth-and-death Markov evolutions on $\mathbb{R}^d$ are obtained as unique weak solutions to the associated Fokker-Planck equations. Such solutions are constructed by its associated sequence of correlation functions satisfying the so-called Ruelle-bound. Using the general scheme of Vlasov scaling we are able to derive a system of non-linear, non-local mesoscopic equations describing the effective density of the particle system. The results are applied to several models of ecology and biology.

### Fredholm theory connected with a Douglis-Nirenberg system of differential equations over $\mathbb{R}^n$

Methods Funct. Anal. Topology **22** (2016), no. 4, 330-345

We consider a spectral problem over $\mathbb{R}^n$ for a Douglis-Nirenberg system of differential operators under limited smoothness assumptions and under the assumption of parameter-ellipticity in a closed sector $\mathcal{L}$ in the complex plane with vertex at the origin. We pose the problem in an $L_p$ Sobolev-Bessel potential space setting, $1 < p < \infty$, and denote by $A_p$ the operator induced in this setting by the spectral problem. We then derive results pertaining to the Fredholm theory for $A_p$ for values of the spectral parameter $\lambda$ lying in $\mathcal{L}$ as well as results pertaining to the invariance of the Fredholm domain of $A_p$ with $p$.

### Poisson measure as a spectral measure of a family of commuting selfadjoint operators, connected with some moment problem

Methods Funct. Anal. Topology **22** (2016), no. 4, 311-329

It is proved that the Poisson measure is a spectral measure of some family of commuting selfadjoint operators acting on a space constructed from some generalization of the moment problem.