Global hypoellipticity of systems of Fourier multipliers on compact Lie groups

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