Global hypoellipticity of systems of Fourier multipliers on compact Lie groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911020074663936 |
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| author | Kowacs, André Pedroso |
| author_facet | Kowacs, André Pedroso |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global hypoellipticity of systems of Fourier multipliers on compact Lie groups Kowacs, André Pedroso Analysis of PDEs 22E30, 43A77, 58J40 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. |
| title | Global hypoellipticity of systems of Fourier multipliers on compact Lie groups |
| topic | Analysis of PDEs 22E30, 43A77, 58J40 |
| url | https://arxiv.org/abs/2505.16958 |