Mathematics

Projective and injective descriptions in the complex domain. Duality

Authors: Shishkin A. B.

Research of a invariant subspaces of a differential operators infinite order in a complex domain generated many issues, related with transition to dual problems. This work devoted overcome these difficulties 

On an inverse problem for differential operators on hedgehog-type graphs

Authors: Yurko V. A.

An inverse spectral problem is studied for Sturm–Liouville differential operators on hedgehog-type graphs with generalized matching conditions in the interior vertices and with Dirichlet boundary conditions in the boundary vertices. A uniqueness theorem of recovering potentials from given spectral characteristics is provided, and a constructive solution for the inverse problem is obtained. 

About harmonic analysis of periodic at infinity functions

Authors: Strukova I. I.

We consider slowly varying and periodic at infinity multivariable functions in Banach space. We introduce the notion of Fourier series of periodic at infinity function, study the properties of Fourier series and their convergence. Basic results are derived with the use of isometric representations theory. 

Mixed problem for simplest hyperbolic first order equations with involution

Authors: Burlutskaya M. S., Khromov A. P.

In this paper investigates the mixed problem for the first order differential equation with involution at the potential and with periodic boundary conditions. Using the received refined asymptotic formulas for eigenvalues and eigenfunctions of the corresponding spectral problem, the application of the Fourier method is substantiated. We used techniques, which allow to avoid investigation of the uniform convergence of the series, obtained by term by term differentiation of formal solution on method of Fourier.

Well-posedness of the Dirichlet problem in a cylindrical domain for multidimensional elliptic-parabolic equation

Authors: Aldashev S. A.

A unique solvability of classic solutions to Dirichlet's problem in the cylindrical domain for the model multidimensional elliptic-parabolic equation is shown in the article