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

2025/06/13 by Fernando de Ávila Silva, Marco Cappiello, Silva, Fernando de Ávila +3 · 1 citation
Mathematics · Physics and Astronomy · #35B10 #35H10 #35N10 #46F05 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2506.12178

openalex publication_date 2025/06/13 · openalex created_date 2025/10/13 · openalex updated_date 2026/07/28

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.

Citations

• Systems of differential operators in time-periodic Gelfand-Shilov spaces
• Globally solvable time-periodic evolution equations in Gelfand-Shilov classes
• Some remarks on the Cauchy Problem for Schrödinger type equations in Gelfand-Shilov spaces
• The Cauchy problem for 3-evolution equations with data in Gelfand-Shilov spaces
• Schrödinger-type equations in Gelfand-Shilov spaces
• Semilinear pseudodifferential equations in spaces of tempered ultradistributions
• Gabor representations of evolution operators

Cited by

• Differential complexes in time-periodic Gelfand-Shilov spaces

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