Factorization of Scalar Piecewise Continuous Almost Periodic Functions

TL;DR

This paper characterizes piecewise continuous almost periodic functions as products of Bohr almost periodic functions and sequences, and applies this to analyze solutions of impulsive differential equations.

Contribution

It introduces a novel factorization of piecewise continuous almost periodic functions and applies it to impulsive differential equations.

Findings

Characterization of piecewise continuous almost periodic functions as products.

Application to impulsive differential equations.

Insight into the structure of almost periodic solutions.

Abstract

This paper is to characterize piecewise continuous almost periodic functions as the product of Bohr almost periodic functions and sequences. As an application, the result is used to discuss piecewise continuous almost periodic solutions of impulsive differential equations.