# almost periodic at infinity functions

## The research of some classes of almost periodic at infinity functions

The article under consideration is devoted to continuous almost periodic at infinity functions defined on the whole real axis and with their values in a complex Banach space. We consider different subspaces of functions vanishing at infinity, not necessarily tending to zero at infinity. We introduce the notions of slowly varying and almost periodic at infinity functions with respect to these subspaces. For almost periodic at infinity functions (with respect to a subspace) we give four different definitions.

## Almost Periodic at Infinity Functions Relative to the Subspace of Functions Integrally Decrease at Infinity

In the paper we introduce and study a new class of almost periodic at infinity functions, which is defined by means of a subspace of integrally decreasing at infinity functions. It is wider than the class of almost periodic at infinity functions introduced in the papers of A.G.Baskakov (with respect to the subspace of functions vanishing at infinity).