Analysis reveals conditions for global hypoellipticity of left-invariant operators on compact Lie groups, indicating broader applications.
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.
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André Pedroso Kowacs (2025) studied this question.
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