Global Hypoellipticity on Time-Periodic Gelfand-Shilov Spaces Via Non-Discrete Fourier Analysis

Abstract In this paper, we provide a characterization of the time-periodic Gelfand-Shilov spaces, as introduced by F. de Ávila Silva and M. Cappiello, J. Funct. Anal. , 2022, through the asymptotic behaviour of both the Euclidean and periodic partial Fourier transforms of their elements. As an application, we establish necessary and sufficient conditions for global regularity—within this framework—for a broad class of constant-coefficient differential operators, as well as for first-order tube-type operators.