On integral equations in mean values in spaces of almost periodic functions (Q1901959)

We study the properties of the operator \[ \widetilde K \varphi (t) = \lim_{T \to \infty} (2T)^{-1} \int^T_{-T} K(t,s) \varphi (s)ds \tag{1} \] in spaces of almost periodic functions introduced by Bohr, Stepanov, Weyl, and Besicovitch. We introduce the generalized discrete Fourier transformation in the Besicovitch space \(B^2\) of almost periodic functions and study properties of such a transformation. We solve certain integral and integro-differential equations with operators of the form (1).