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This is a Quantitative Study study.

October 20, 2025Open Access

Global hypoellipticity of systems of Fourier multipliers on compact Lie groups

Puntos clave

A necessary and sufficient condition for global hypoellipticity of left-invariant operators was established.
The study provides independent proof independent of previous bundle structure analyses.
Alternative sufficient conditions for globally hypoellipticity leverage lower bounds on singular values.
These findings contribute to a deeper understanding of operator behavior on compact Lie groups.

Resumen

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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Cite This Study

André Pedroso Kowacs (Thu,) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac36130 https://doi.org/https://doi.org/10.48550/arxiv.2505.16958

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