New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results and applications

Abstract

The aim of this work is to present new approach to study weighted pseudo almost periodic functions using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions like completeness and composition theorems. The theory of this work generalizes the classical results on weighted pseudo almost periodic functions. For illustration, we provide some applications for evolution equations which include reaction diffusion systems and partial functional differential equations.

Keywords:

• measure theory
• ergodicity
• μ-pseudo almost periodic function
• completeness and composition theorem
• evolution equations
• reaction diffusion system
• partial functional differential equations

AMS Subject Classifications:

• 34K14
• 34K30
• 35B15
• 35K57
• 44A35
• 47D06

Acknowledgements

The authors would like to thank the referees for their careful reading of this article. Their valuable suggestions and critical remarks made numerous improvements throughout this article.