We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover, we prove an existence theorem for the weighted pseudo almost-periodic mild solution to the semilinear evolution equation: x′ (t) = A x (t) + f (t, x (t)), t ∈ R , where A is the infinitesimal generator of an exponentially stable C 0 -semigroup. An application is also given to illustrat...
