slowly varying at infinity function

Harmonic Analysis of Operator Semigroups Slowly Varying at Infinity

Authors: Strukov V. E., Strukova I. I.

The article focuses on studying of strongly continuous bounded operator semigroups. In the space of uniformly continuous functions with values inacomplex Banach space weconsider the subspace of integrally vanishing at infinity functions. This subspace includes the subspace of vanishing at infinity functions, but it is wider. We study the properties of the subspace under consideration.

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.

Qualitative Properties of Mild Solutions of the Cauchy Problem

Authors: Kaluzhina N. S.

In this paper we study the qualitative properties of a mild solution of the problem Cauchy problem for the heat equation. We prove that every mild Cauchy problem is a slowly varying at infinity function.
The result is applied to study solutions of the Neumann problem for the heat equation.