Almost Automorphy of the Convolution Operator and Applications to Differential and Functional Differential Equations

Abstract

We discuss conditions which do ensure the almost automorphy of the convolution function $f\star h$ of f with h where f is almost automorphic and h is a (Lebesgue) measurable function satisfying some additional assumptions. Next we make extensive use of the obtained result to examine almost automorphic solutions to some differential and functional equations as well as a Volterra-like equation.