A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G. The notion of density arises naturally both in connection with the theory of uniform distribution and with the theory of almost periodic functions. Our main result effectively answers the question "when are all densities on G induced by measures on some compactification of G?...

In this note we communicate some important remarks about the concepts of almost periodic time scales and almost periodic functions on time scales that are proposed by Wang and Agarwal in their recent papers ( see [7]-[10]).

We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their wellposedness and describe some qualitative properties of their solutions, including boundedness, stability, or almost periodicity. In particular, we are able to characterize the analyticity of ...

For the complete higher order differential equation u(t) = Σn−1 k=0Aku (t) + f(t), t ∈ R (*) on a Banach space E, we give a new definition of mild solutions of (*). We then characterize the regular admissibility of a translation invariant subspace M of BUC(R,E) with respect to (*) in terms of solvability of the operator equation Σn−1 j=0AjXD j −XD = C. As application, almost periodicity of mild...