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arXiv · 2506.13475

Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis

André Pedroso Kowacs·Pedro Meyer Tokoro
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Abstract

In this paper, we provide a characterization of the time-periodic Gelfand-Shilov spaces, as introduced by F. de \'Avila Silva and M. Cappiello [J. Funct. Anal., 282(9):29, 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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André Pedroso Kowacs, Pedro Meyer Tokoro. 2025-06-16. Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis. https://doi.org/10.1007/s00041-026-10253-3

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