Banach space

Linear Difference Equation of Second Order in a Banach Space and Operators Splitting

Authors: Kabantsova L. Y.

In differential and difference equations classical textbooks, the n-th order differential and difference equations reducing by standard substitution to first-order differential and difference equations system is described. Each of the cohering equations can be written in the operator form. Naturally there is a question of coincidence of a number of properties of differential and difference equations (operators) of the second order and the corresponding functional equations (operators) of first order.

Harmonic Analysis of Periodic at Infinity Functions from Stepanov Spaces

Authors: Strukova I. I.

We consider Stepanov spaces of functions defined on R with their values in a complex Banach space. We introduce the notions of slowly varying and periodic at infinity functions from Stepanov space. The main results of the article are concerned with harmonic analysis of periodic at infinity functions from Stepanov space. For this class of functions we introduce the notion of a generalized Fourier series; the Fourier coefficients in this case may not be constants, they are functions that are slowly varying at infinity.

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. 

Wiener's theorem for periodic at infinity functions

Authors: Strukova I. I.

 In this article banach algebra of periodic at infinity functions is defined. For this class of functions notions of Fourier series and absolutely convergent Fourier series are introduced. As a result Wiener's theorem analog devoted to absolutely convergent Fourier series for periodic at infinity functions was proved. 

Structure of the inverse for the integral operator of special kind

Authors: Strukov V. E.

Algebra (with identity) generated by integral operators on the spaces of continuous periodic functions is considered. This algebra is proved to be an inverse-closed subalgebra in the algebra of all bounded linear operators.