# Methods of Functional Analysis

and Topology

Editors-in-Chief: A. N. Kochubei,
Yu. G. Kondratiev

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

Founded by Yu. M. Berezansky in 1995.

Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed 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, Scopus, Web of Science, DOAJ, Google Scholar

## Latest Articles (December, 2019)

### Essential approximate point and essential defect spectrum of a sequence of linear operators in Banach spaces

Toufik Heraiz, Aymen Ammar, Aref Jeribi

Methods Funct. Anal. Topology **25** (2019), no. 4, 373-380

This paper is devoted to an investigation of the relationship between the essential approximate point spectrum (respectively, the essential defect spectrum) of a sequ\-ence of closed linear operators $(T_n)_{n\in\mathbb{N}}$ on a Banach space $X$, and the essential approximate point spectrum (respectively, the essential defect spectrum) of a linear operator $T$ on $X$, where $(T_n)_{n\in\mathbb{N}}$ converges to $T$, in the case of convergence in generalized sense as well as in the case of the convergence compactly

### Approximation by Fourier sums in classes of differentiable functions with high exponents of smoothness

A. S. Serdyuk, I. V. Sokolenko

Methods Funct. Anal. Topology **25** (2019), no. 4, 381-387

We find asymptotic equalities for the exact upper bounds of approximations by Fourier sums of Weyl-Nagy classes $W^r_{\beta,p}, 1\le p\le\infty,$ for rapidly growing exponents of smoothness $r$ $(r/n\rightarrow\infty)$ in the uniform metric. We obtain similar estimates for approximations of the classes $W^r_{\beta,1}$ in metrics of the spaces $L_p, 1\le p\le\infty$.

### Point spectrum in conflict dynamical systems with fractal partition

V. Koshmanenko, O. Satur, V. Voloshyna

Methods Funct. Anal. Topology **25** (2019), no. 4, 324-338

We discuss the spectral problem for limit distributions of conflict dynamical systems on spaces subjected to fractal divisions. Conditions ensuring the existence of the point spectrum are established in two cases, the repulsive and the attractive interactions between the opponents. A key demand is the strategy of priority in a single region.

### Three spectra problems for star graph of Stieltjes strings

Methods Funct. Anal. Topology **25** (2019), no. 4, 311-323

The (main) spectral problem for a star graph with three edges composed of Stieltjes strings is considered with the Dirichlet conditions at the pendant vertices. In addition we consider the Dirichlet-Neumann problem on the first edge (Problem 2) and the Dirichlet-Dirichlet problem on the union of the second and the third strings (Problem 3). It is shown that the spectrum of the main problem interlace (in a non-strict sense) with the union of spectra of Problems 2 and 3. The inverse problem lies in recovering the masses of the beads (point masses) and the lengths of the intervals between them using the spectra of the main problem and of Problems 2 and 3. Conditions on three sequences of numbers are proposed sufficient to be the spectra of the main problem and of Problems 2 and 3, respectively.