This analysis establishes conditions for global regularity in differential operators within periodic function spaces, suggesting implications for mathematical modeling.
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.
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Kowacs et al. (2026) studied this question.