Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations

Abstract

The aim of this work is to give sufficient conditions ensuring that the space PAP(𝕉, X, µ) of µ-pseudo almost periodic functions and the space PAA(𝕉, X, µ) of µ-pseudo almost automorphic functions are invariant by the convolution product f = k * f, k ∈ L1(𝕉). These results establish sufficient assumptions on k and the measure µ. As a consequence, we investigate the existence and uniqueness of µ-pseudo almost periodic solutions and µ-pseudo almost automorphic solutions for some abstract integral equations, evolution equations and partial functional differential equations.

Keywords

• measure theory
• µ-ergodic
• µ-pseudo almost periodic functions
• µ-pseudo almost automorphic functions
• integral equations
• evolution equations
• partial functional differential equations
• reaction-diffusion systems
• 34c27
• 34k14
• 35b15
• 35k57
• 37a30