A connection between almost periodic functions defined on timescales and ℝ

Abstract

In this paper, we prove a strong connection between almost periodic functions on timescales and almost periodic functions on . An application to difference equations on is given.

Keywords:

• almost periodic functions
• timescales
• dynamic equations
• difference equations

AMS Subject Classifications:

• 42A75
• 34N05
• 26E70

Acknowledgements

The authors are grateful to the referee for several useful comments and valuable suggestions in order to improve a previous version of this paper.

Notes

The first and third authors are partially supported by project PIA-CONICYT ACT 1112: Red de Análisis Estocástico y Aplicaciones. The second author is supported by CAPES [grant number 5811/12-0].