# 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, DOAJ, Google Scholar.

## Latest Articles (December, 2017)

### Representation of isometric isomorphisms between monoids of Lipschitz functions

Methods Funct. Anal. Topology **23** (2017), no. 4, 309-319

We prove that each isometric isomorphism between the monoids of all nonnegative $1$-Lipschitz maps defined on invariant metric groups and equipped with the inf-convolution law, is given canonically from an isometric isomorphism between their groups of units.

### Localization principles for Schrödinger operator with a singular matrix potential

Vladimir Mikhailets, Aleksandr Murach, Viktor Novikov

Methods Funct. Anal. Topology **23** (2017), no. 4, 367-377

We study the spectrum of the one-dimensional Schrödinger operator $H_0$ with a matrix singular distributional potential $q=Q'$ where $Q\in L^{2}_{\mathrm{loc}}(\mathbb{R},\mathbb{C}^{m})$. We obtain generalizations of Ismagilov's localization principles, which give necessary and sufficient conditions for the spectrum of $H_0$ to be bounded below and discrete.

### Weak and vague convergence of spectral shift functions of one-dimensional Schrödinger operators with coupled boundary conditions

Methods Funct. Anal. Topology **23** (2017), no. 4, 378-403

We prove weak and vague convergence results for spectral shift functions associated with self-adjoint one-dimensional Schrödinger operators on intervals of the form $(-\ell,\ell)$ to the full-line spectral shift function in the limit $\ell\to \infty$ for a class of coupled boundary conditions. The boundary conditions considered here include periodic boundary conditions as a special case.

### Spectral properties and stability of a nonselfadjoint Euler-Bernoulli beam

Methods Funct. Anal. Topology **23** (2017), no. 4, 346-366

In this note we study the spectral properties of an Euler-Bernoulli beam model with damping and elastic forces applying both at the boundaries as well as along the beam. We present results on completeness, minimality, and Riesz basis properties of the system of eigen- and associated vectors arising from the nonselfadjoint spectral problem. Within the semigroup formalism it is shown that the eigenvectors have the property of forming a Riesz basis, which in turn enables us to prove the uniform exponential decay of solutions of the particular system considered.