On Bochner's Almost-periodicity criterion

TL;DR

This paper extends Bochner's criterion for almost periodic functions, providing new tools for analyzing periodic dynamical systems and characterizing periodic functions more broadly.

Contribution

The authors introduce an extended version of Bochner's criterion, enhancing its applicability to periodic dynamical systems and offering a new characterization of periodic functions.

Findings

Extended Bochner's criterion for almost periodic functions

Generalization useful for periodic dynamical systems

New characterization of periodic functions

Abstract

We give an extension of Bochner's criterion for the almost periodic functions. By using our main result, we extend two results of A. Haraux. The first is a generalization of Bochner's criterion which is useful for periodic dynamical systems. The second is a characterization of periodic functions in term of Bochner's criterion.