Compactifications, Hartman functions and (weak) almost periodicity

Compactifications, Hartman functions and (weak) almost periodicity

In this paper we investigate Hartman functions on a topological group G. Recall that (ι, C) is a group compactification of G if C is a compact group, ι : G → C is a continuous group homomorphism and ι(G) ⊆ C is dense. A bounded function f : G 7→ C is a Hartman function if there exists a group compactification (ι, C) and F : C → C such that f = F ◦ ι and F is Riemann integrable, i.e. the set of ...

m at h . FA ] 1 7 D ec 2 00 7 Compactifications , Hartman functions and ( weak ) almost periodicity

In this paper we investigate Hartman functions on a topological group G. Recall that (ι, C) is a group compactification of G if C is a compact group, ι : G → C is a continuous group homomorphism and ι(G) ⊆ C is dense. A bounded function f : G 7→ C is a Hartman function if there exists a group compactification (ι, C) and F : C → C such that f = F ◦ ι and F is Riemann integrable, i.e. the set of ...

SEMIGROUP ACTIONS , WEAK ALMOST PERIODICITY, AND INVARIANT MEANS

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

On Hartman Almost Periodic Functions

In this note we consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in R or Z. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally co...

Periodicity and Almost-periodicity