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arXiv · 2403.05096

Systems of differential operators in time-periodic Gelfand-Shilov spaces

Fernando de Ávila Silva·Marco Cappiello·Alexandre Kirilov
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Abstract

This paper explores the global properties of time-independent systems of operators in the framework of Gelfand-Shilov spaces. Our main results provide both necessary and sufficient conditions for global solvability and global hypoellipticity, based on analysis of the symbols of operators. We also present a class of time-dependent operators whose solvability and hypoellipticity are linked to the same properties of an associated time-independent system, albeit with a loss of regularity for temporal variables.

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Fernando de Ávila Silva, Marco Cappiello, Alexandre Kirilov. 2024-03-08. Systems of differential operators in time-periodic Gelfand-Shilov spaces. https://arxiv.org/abs/2403.05096

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