We examine conditions which do ensure the asymptotic almost periodicity (respectively, pseudo almost periodicity) of the convolution function of with whenever is asymptotically almost periodic (respectively, pseudo almost periodic) and 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.
Cite this article
Dariusz Bugajewski, Toka Diagana, Crépin M. Mahop, Asymptotic and Pseudo Almost Periodicity of the Convolution Operator and Applications to Differential and Integral Equations. Z. Anal. Anwend. 25 (2006), no. 3, pp. 327–340DOI 10.4171/ZAA/1292