Hypoellipticity and solvability of systems of strongly invariant operators on Komatsu classes

In this paper, we investigate systems of strongly invariant operators acting on Komatsu ultradifferentiable classes over compact manifolds without boundary. Using the eigenfunction expansion associated with a positive elliptic pseudo-differential operator E , we establish necessary and sufficient conditions for global hypoellipticity and global solvability in Komatsu ultradifferentiable classes. These characterizations are given in terms of precise lower bounds on the matrix symbol associated with the system of operators. As an application of the general theory, we consider vector fields and systems of vector fields on compact Lie groups, illustrating how the abstract results apply to concrete differential operators arising in this setting.