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arXiv · 2505.16958

Global hypoellipticity of systems of Fourier multipliers on compact Lie groups

André Pedroso Kowacs
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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.

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André Pedroso Kowacs. 2025-05-22. Global hypoellipticity of systems of Fourier multipliers on compact Lie groups. https://arxiv.org/abs/2505.16958

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