JournalszaaVol. 25 , No. 3DOI 10.4171/zaa/1292

Asymptotic and Pseudo Almost Periodicity of the Convolution Operator and Applications to Differential and Integral Equations

  • Dariusz Bugajewski

    Adam Mickiewicz University, Poznan, Poland
  • Toka Diagana

    Howard University, Washington, United States
  • Crépin M. Mahop

    Howard University, Washington, United States
Asymptotic and Pseudo Almost Periodicity of the Convolution Operator and Applications to Differential and Integral Equations cover

Abstract

We examine conditions which do ensure the asymptotic almost periodicity (respectively, pseudo almost periodicity) of the convolution function fhf \ast h of ff with hh whenever ff is asymptotically almost periodic (respectively, pseudo almost periodic) and hh is a (Lebesgue) measurable function satisfying some additional assumptions. Next we make extensive use of those results to investigate on the asymptotically almost periodic (respectively, pseudo almost periodic) solutions to some differential, functional, and integral equations.