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arXiv · 2506.12178

Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces

Fernando de Ávila Silva·Marco Cappiello·Alexandre Kirilov
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Abstract

We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and sufficient conditions for the global hypoellipticity of this class of systems, stated in terms of Diophantine-type estimates and sign-changing behavior of the imaginary parts of the coefficients. Through a reduction to a normal form and detailed construction of singular solutions, we fully characterize when the system fails to be globally hypoelliptic.

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Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov. 2025-06-13. Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces. https://arxiv.org/abs/2506.12178

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