# 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

### Non-autonomous systems on Lie groups and their topological entropy

Methods Funct. Anal. Topology **25** (2019), no. 4, 360-372

In the present paper we introduce and study the topological entropy of non-autonomous dynamical systems and define the non-autonomous dynamical system on Lie groups and manifolds. Our main purpose is to estimate the topological entropy of the non-autonomous dynamical system on Lie groups. We show that the topological entropy of the non-autonomous dynamical system on Lie groups and induced Lie algebra are equal under topological conjugacy, and a method to estimate the topological entropy of non-autonomous systems on Lie groups is given. To illustrate our results, some examples are presented. Finally some discussions and comments about positive entropy on nil-manifold Lie groups for non-autonomous systems are presented.

### Analyticity and other properties of functionals $I\left(f, p\right)=\int_{A}|f(t)|^p dt$ and $n(f,p)=\left(\frac{1}{\mu(A)}\int_{A}|f(t)|^p dt\right)^{\frac{1}{p}}$ as functions of variable $p$

Methods Funct. Anal. Topology **25** (2019), no. 4, 339-359

We showed that for each function $f(t)$, which is not equal to zero almost everywhere in the Lebesgue measurable set, functionals $I\left(f,z\right)=\int_A{{|f(t)|}^z dt}$ as functions of a complex variable $z=p+iy$ are continuous on the domain and analytic on a set of all inner points of this domain. The functions $I(f,p)$ as functions of a real variable $ p $ are strictly convex downward and log-convex on the domain. We proved that functionals $n(f,p)$ as functions of a real variable $p$ are analytic at all inner points of the interval, in which the function $n(f,p)\neq 0$ except the point $p=0$, continuous and strictly increasing on this interval.

### 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.