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., 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.
Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis
Pedro Meyer Tokoro
2025-01-01
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., 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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