Global hypoellipticity of systems of Fourier multipliers on compact Lie groups

2025/05/22 by André Pedroso Kowacs, Kowacs, André Pedroso
Mathematics · #22E30 #43A77 #58J40 #Advanced Algebra and Geometry #Analysis of PDEs (math.AP) #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2505.16958

openalex publication_date 2025/05/22 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We apply the characterization of global hypoellipticity for G-invariant operators on homogeneous vector bundles obtained by Cardona and Kowacs [J. Pseudo-Differ. Oper. Appl. 16, 23 (2025)] to obtain a necessary and sufficient condition for an arbitrary system of left-invariant operators on a compact Lie group to be globally hypoelliptic, providing a full proof independent of the bundle structure of that paper. We then prove alternative sufficient conditions for globally hypoellipticity for a large class of particular cases of systems making use of lower bounds for the smallest singular value of complex matrices.

Citations

• Global Hypoellipticity and Solvability with Loss of Derivatives on the Torus
• Global solutions for systems of strongly invariant operators on closed manifolds
• Diagonal systems of differential operators on compact Lie groups
• Pseudo-differential operators on Homogeneous vector bundles over compact homogeneous manifolds
• Systems of differential operators in time-periodic Gelfand-Shilov spaces
• Global hypoellipticity of G-invariant operators on homogeneous vector bundles
• Global hypoellipticity for a class of overdetermined systems of pseudo-differential operators on the torus
• Globally hypoelliptic triangularizable systems of periodic pseudo-differential operators
• Local and global symbols on compact Lie groups
• Intrinsic pseudodifferential calculi on any compact Lie group

Related

• Global hypoellipticity of G-invariant operators on homogeneous vector bundles
• A class of globally analytic hypoelliptic operators on compact Lie groups
• Global hypoellipticity for a class of complex-valued evolution equations on compact Lie groups
• Diagonal systems of differential operators on compact Lie groups
• Global analytic hypoellipticity and solvability of certain operators subject to group actions