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

2024/03/08 by Silva, Fernando de Ávila, Cappiello, Marco, Kirilov, Alexandre · 3 citations
#35A01. Secondary 35H10 #46F05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35N05

paper · doi:10.48550/arxiv.2403.05096

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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