Systems of differential operators in time-periodic Gelfand-Shilov spaces
arxiv(2024)
摘要
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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