Global solutions for systems of strongly invariant operators on closed manifolds

2025/02/25 by Kirilov, Alexandre, de Moraes, Wagner Augusto Almeida, Tokoro, Pedro Meyer · 1 citation
#35H10 Secondary 47A15 #35P15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 58J40

paper · doi:10.48550/arxiv.2502.18660

Abstract

We study the global hypoellipticity and solvability of strongly invariant operators and systems of strongly invariant operators on closed manifolds. Our approach is based on the Fourier analysis induced by an elliptic pseudo-differential operator, which provides a spectral decomposition of L²(M) into finite-dimensional eigenspaces. This framework allows us to characterize these global properties through asymptotic estimates on the matrix symbols of the operators. Additionally, for systems of normal strongly invariant operators, we derive an explicit solution formula and establish sufficient conditions for global hypoellipticity and solvability in terms of their eigenvalues.

Cited by

• Directional Poincaré inequality on compact Lie groups
• Global hypoellipticity of systems of Fourier multipliers on compact Lie groups

Related

• Global ultradifferentiable hypoellipticity on compact manifolds
• Global analytic hypoellipticity and solvability of certain operators subject to group actions
• Global Solvability for Involutive Systems on Non-Compact Manifolds
• Global hypoellipticity of systems of Fourier multipliers on compact Lie groups
• Diagonal systems of differential operators on compact Lie groups