Global hypoellipticity for a class of time-periodic operators on asymptotically Euclidean manifolds

We introduce time-periodic Gevrey-Sobolev-Kato spaces on asymptotically Euclidean manifolds and study their characterisation throughout Fourier expansions associated with suitable elliptic operators. As an application, we study the global hypoellipticity problem for a naturally associated class of time-periodic evolution equations.