# 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 (ESCI), Google Scholar.

## Latest Articles (March, 2017)

### On Fourier algebra of a hypergroup constructed from a conditional expectation on a locally compact group

A. A. Kalyuzhnyi, G. B. Podkolzin, Yu. A. Chapovsky

Methods Funct. Anal. Topology **23** (2017), no. 1, 37-50

We prove that the Fourier space of a hypergroup constructed from a conditional expectation on a locally compact group has a Banach algebra structure.

### On certain spectral features inherent to scalar type spectral operators

Methods Funct. Anal. Topology **23** (2017), no. 1, 60-65

Important spectral features such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at 0, known to hold for bounded scalar type spectral operators, are shown to naturally transfer to the unbounded case.

### Sturm-Liouville operators with matrix distributional coefficients

Alexei Konstantinov, Oleksandr Konstantinov

Methods Funct. Anal. Topology **23** (2017), no. 1, 51-59

The paper deals with the singular Sturm-Liouville expressions $$l(y) = -(py')' + qy$$ with the matrix-valued coefficients $p,q$ such that $$q=Q', \quad p^{-1},\, p^{-1}Q, \,\, Qp^{-1}, \,\, Qp^{-1}Q \in L_1, $$ where the derivative of the function $Q$ is understood in the sense of distributions. Due to a suitable regularization, the corresponding operators are correctly defined as quasi-differentials. Their resolvent convergence is investigated and all self-adjoint, maximal dissipative, and maximal accumulative extensions are described in terms of homogeneous boundary conditions of the canonical form.

### Tannaka-Krein reconstruction for coactions of finite quantum groupoids

Leonid Vainerman, Jean-Michel Vallin

Methods Funct. Anal. Topology **23** (2017), no. 1, 76-107

We study coactions of finite quantum groupoids on unital $C^*$-algebras and obtain a Tannaka-Krein reconstruction theorem for them.