Differential and pseudodifferential operators in spaces of almost periodic functions

We construct a Sobolev-type space of almost periodic functions, in which we study differential and pseudodifferential operators. We show that the usual theorem on the regularity of solutions of elliptic equations is not true in these spaces, and we present modified variants of this theorem. We also study the question of the defect indices of differential operators in the space of Besicovitch almost periodic functions, and prove a Liouville-type theorem in this space.
Bibliography: 16 titles.