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Zeitschrift für Analysis und ihre Anwendungen


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Volume 25, Issue 3, 2006, pp. 327–340
DOI: 10.4171/ZAA/1292

Published online: 2006-09-30

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

Dariusz Bugajewski[1], Toka Diagana[2] and Crépin M. Mahop[3]

(1) Adam Mickiewicz University, Poznan, Poland
(2) Howard University, Washington, United States
(3) Howard University, Washington, United States

We examine conditions which do ensure the asymptotic almost periodicity (respectively, pseudo almost periodicity) of the convolution function $f \ast h$ of $f$ with $h$ whenever $f$ is asymptotically almost periodic (respectively, pseudo almost periodic) and $h$ 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.

Keywords: Almost periodic function, asymptotically almost periodic function, Banach fixed-point principle, convolution operator, differential equation, integral equation, functional equation, pseudo almost periodic function, Zima's fixed-point theorem

Bugajewski Dariusz, Diagana Toka, Mahop Crépin: Asymptotic and Pseudo Almost Periodicity of the Convolution Operator and Applications to Differential and Integral Equations. Z. Anal. Anwend. 25 (2006), 327-340. doi: 10.4171/ZAA/1292