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<p>In this paper, we provide a characterization of the time-periodic Gelfand-Shilov spaces, as introduced by F. de Ávila Silva and M. Cappiello, <i>J. Funct. Anal.</i>, 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月2日

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  • André Pedroso Kowacs,
  • Pedro M. Tokoro

摘要

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.