On Some Properties of Functions Almost Periodic at Infinity from Homogeneous Spaces

摘要

Abstract In this paper, we consider homogeneous spaces of functions defined on the whole real axis with values in a complex Banach space. A new class of functions from a homogeneous space that are almost uniformly periodic at infinity is introduced and examined. Four definitions of such functions are proposed and their equivalence is proved. Fourier series of functions almost periodic at infinity are constructed and their properties are analyzed. In this paper, we essentially used results of the theory of isometric representations and the theory of Banach modules.