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Some remarks on almost periodic functions

Adamczak M.

Fasciculi Mathematici

2002

Nr 33

5-19

In this paper we present the definition and some properties of (IC)-a.p. functions, i.e. uniformly almost periodic (IC)(n)-a.p. functions with their indefinite integrals. Next, we give the definition and some properties of (IC)(n) -a.p. functions, i.e. uniformly almost periodic functions with their n derivatives and indefinite indegrals, and (IC)(n) -a.p. functions, i.e. uniformly almost periodic functions with their every derivatives, with respect to a positive sequence a = (a1), and indefinite integrals.

Some remarks on spaces of almost periodic functions

Stoiński S.

Fasciculi Mathematici

2001

Nr 31

105-115

In this note we present remarks on completeness of spaces of almost periodic functions of various types and some theorems on connection between almost periodicity of the derivative and the indefinite integral of the function and almost periodicity of the function.

N- almost periodic in the sense of variation functions

Stoiński S.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2001

[Z] 41

195-202

In this paper we present the definitions and some theorems on (N,V) - almost periodic (a.p.) functions (N,S^p)-a.p. functions and (N,V_p)-a.p. functions. We prove that if f is an (N,S)-a.p. function and the indefinite integral F of f is bounded, them F is (N,V)-a.p.

On the indefinite integral and approximation of H-almost periodic functions

Stoiński S.

Fasciculi Mathematici

1999

Nr 29

133-137

The paper gives a theorem on the indefinite integral of H-almost periodic function and a theorem on approximation of an H-almost periodic function by means Steklov functions.

On compactness of C(n)-almost periodic functions

Adamczak M.

Demonstratio Mathematica

1999

Vol. 32, nr 2

385-400

In this paper we give a compactness criterion for C(n)-almost periodic functions. Some properties of these functions are shown.