# 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, Scopus, Web of Science, DOAJ, Google Scholar

## Latest Articles (March, 2019)

### Boundary triples for integral systems on the half-line

Methods Funct. Anal. Topology **25** (2019), no. 1, 84-96

Let $P$, $Q$ and $W$ be real functions of locally bounded variation on $[0,\infty)$ and let $W$ be non-decreasing. In the case of absolutely continuous functions $P$, $Q$ and $W$ the following Sturm-Liouville type integral system: \begin{equation} \label{eq:abs:is} J\vec{f}(x)-J\vec{a} = \int_0^x \begin{pmatrix}\lambda dW-dQ & 0\\0 & dP\end{pmatrix} \vec{f}(t), \quad J = \begin{pmatrix}0 & -1\\1 & 0\end{pmatrix} \end{equation} (see [5]) is a special case of so-called canonical differential system (see [16, 20, 24]). In [27] a maximal $A_{\max}$ and a minimal $A_{\min}$ linear relations associated with system (1) have been studied on a compact interval. This paper is a continuation of [27] , it focuses on a study of $A_{\max}$ and $A_{\min}$ on the half-line. Boundary triples for $A_{\max}$ on $[0,\infty)$ are constructed and the corresponding Weyl functions are calculated in both limit point and limit circle cases at $\infty$.

### Measure of noncompactness, essential approximation and defect pseudospectrum

Aymen Ammar, Aref Jeribi, Kamel Mahfoudhi

Methods Funct. Anal. Topology **25** (2019), no. 1, 1-11

The scope of the present research is to establish some findings concerning the essential approximation pseudospectra and the essential defect pseudospectra of closed, densely defined linear operators in a Banach space, building upon the notion of the measure of noncompactness. We start by giving a refinement of the definition of the essential approximation pseudospectra and that of the essential defect pseudospectra by means of the measure of noncompactness. From these characterizations we shall deduce several results and we shall give sufficient conditions on the perturbed operator to have its invariance.

### Complex moment problem and recursive relations

Methods Funct. Anal. Topology **25** (2019), no. 1, 15-34

We introduce a new methodology to solve the truncated complex moment problem. To this aim we investigate recursive doubly indexed sequences and their characteristic polynomials. A characterization of recursive doubly indexed \emph{moment} sequences is given. A simple application gives a computable solution to the complex moment problem for cubic harmonic characteristic polynomials of the form $z^3+az+b\overline{z}$, where $a$ and $b$ are arbitrary real numbers. We also recapture a recent result due to Curto-Yoo given for cubic column relations in $M(3)$ of the form $Z^3=itZ+u\overline{Z}$ with $t,u$ real numbers satisfying some suitable inequalities. Furthermore, we solve the truncated complex moment problem with column dependence relations of the form $Z^{k+1}= \sum\limits_{0\leq n+ m \leq k} a_{nm} \overline{Z}^n Z^m$ ($a_{nm} \in \mathbb{C}$).

### On a localization of the spectrum of a complex Volterra operator

Miron B. Bekker, Joseph A. Cima

Methods Funct. Anal. Topology **25** (2019), no. 1, 12-14

A complex Volterra operator with the symbol $g=\log{(1+u(z))}$, where $u$ is an analytic self map of the unit disk $\mathbb D$ into itself is considered. We show that the spectrum of this operator on $H^p(\mathbb D)$, $1\le p<\infty$, is located in the disk $\{\lambda:|\lambda+p/2|\leq p/2\}$.