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

Volumes: 24 | Issues: 90 | Articles: 694 | Authors: 496

Latest Articles (June, 2018)

One-dimensional parameter-dependent boundary-value problems in Hölder spaces

Hanna Masliuk, Vitalii Soldatov

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 24 (2018), no. 2, 143-151

We study the most general class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the complex H\"older space $C^{n+r,\alpha}$, with $0\leq n\in\mathbb{Z}$ and $0<\alpha\leq1$. We prove a constructive criterion under which the solution to an arbitrary parameter-dependent problem from this class is continuous in $C^{n+r,\alpha}$ with respect to the parameter. We also prove a two-sided estimate for the degree of convergence of this solution to the solution of the corresponding nonperturbed problem.

Symmetric extensions of symmetric linear relations (operators) preserving the multivalued part

V. I. Mogilevskii

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 24 (2018), no. 2, 152-177

Let $\mathfrak H$ be a Hilbert space and let $A$ be a symmetric linear relation (in particular, a nondensely defined operator) in $\mathfrak H$. By using the concept of a boundary triplet for $A^*$ we characterize symmetric extensions $\widetilde A\supset A$ preserving the multivalued part of $A$. Such a characterization is given in terms of an abstract boundary parameter and the Weyl function of the boundary triplet. Application of these results to the Hamiltonian system $Jy'-B(t)y=\lambda\Delta(t) y$ enabled us to describe its matrix solutions generating the generalized Fourier transform with the nonempty set of respective spectral functions.

Self-consistent translational motion of reference frames and sign-definiteness of time in universal kinematics

Ya. I. Grushka

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 24 (2018), no. 2, 107-119

Universal kinematics as mathematical objects may be interesting for astrophysics, because there exists a hypothesis that, in the large scale of the Universe, physical laws (in particular, the laws of kinematics) may be different from the laws acting in a neighborhood of our solar System. The present paper is devoted to investigation of self-consistent translational motion of reference frames in abstract universal kinematics. In the case of self-consistent translational motion we can give a clear and unambiguous definition of displacement as well as the average and the instantaneous speed of the reference frame. Hence the uniform rectilinear motion is a particular case of self-consistent translational motion. So, the investigation of self-consistently translational motion is technically necessary for definition of classes of inertially-related reference frames (being in the state of uniform rectilinear mutual motion) in universal kinematics. In the paper we investigate the correlations between self-consistent translational motion and definiteness of time direction for reference frames in universal kinematics.

On the inverse eigenvalue problems for a Jacobi matrix with mixed given data

L. P. Nizhnik

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 24 (2018), no. 2, 178-186

We give necessary and sufficient conditions for existence and uniqueness of a solution to inverse eigenvalues problems for Jacobi matrix with given mixed initial data. We also propose effective algorithms for solving these problems.

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