# 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, open access 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 indexed in: MathSciNet, zbMATH, Google Scholar.

Volumes: 22 | Issues: 82 | Articles: 636 | Authors: 457

## Latest Articles (June, 2016)

### Level sets of asymptotic mean of digits function for $4$-adic representation of real number

Methods Funct. Anal. Topology 22 (2016), no. 2, 184-196

We study topological, metric and fractal properties of the level sets $$S_{\theta}=\{x:r(x)=\theta\}$$ of the function $r$ of asymptotic mean of digits of a number $x\in[0;1]$ in its $4$-adic representation, $$r(x)=\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits^{n}_{i=1}\alpha_i(x)$$ if the asymptotic frequency $\nu_j(x)$ of at least one digit does not exist, were $$\nu_j(x)=\lim_{n\to\infty}n^{-1}\#\{k: \alpha_k(x)=j, k\leqslant n\}, \:\: j=0,1,2,3.$$

### On nonsymmetric rank one singular perturbations of selfadjoint operators

Methods Funct. Anal. Topology 22 (2016), no. 2, 137-151

We consider nonsymmetric rank one singular perturbations of a selfadjoint operator, i.e., an expression of the form $\tilde A=A+\alpha\left\langle\cdot,\omega_1\right\rangle\omega_2$, $\omega_1\not=\omega_2$, $\alpha\in{\mathbb C}$, in a general case $\omega_1,\omega_2\in{\mathcal H}_{-2}$. Using a constructive description of the perturbed operator $\tilde A$, we investigate some spectral and approximations properties of $\tilde A$. The wave operators corresponding to the couple $A$, $\tilde A$ and a series of examples are also presented.

### Inverse moment problem for non-Abelian Coxeter double Bruhat cells

Michael Gekhtman

Methods Funct. Anal. Topology 22 (2016), no. 2, 117-136

We solve the inverse problem for non-Abelian Coxeter double Bruhat cells in terms of the matrix Weyl functions. This result can be used to establish complete integrability of the non-Abelian version of nonlinear Coxeter-Toda lattices in $GL_n$.

### On the generation of Beurling type Carleman ultradifferentiable $C_0$-semigroups by scalar type spectral operators

Marat V. Markin

Methods Funct. Anal. Topology 22 (2016), no. 2, 169-183

A characterization of the scalar type spectral generators of Beurling type Carleman ultradifferentiable $C_0$-semigroups is established, the important case of the Gevrey ultradifferentiability is considered in detail, the implementation of the general criterion corresponding to a certain rapidly growing defining sequence is observed.