Time-periodic Gelfand-Shilov spaces and global hypoellipticity on [formula omitted

Abstract

We introduce a class of time-periodic Gelfand-Shilov spaces of functions on T×Rn, where T∼R/2πZ is the one-dimensional torus. We develop a Fourier analysis inspired by the characterization of the Gelfand-Shilov spaces in terms of the eigenfunction expansions given by a fixed normal, globally elliptic differential operator on Rn. In this setting, as an application, we characterize the global hypoellipticity for a class of linear differential evolution operators on T×Rn.