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math.AP2025
Directional Poincaré inequality on compact Lie groups
Paulo L. Dattori da Silva, André Pedroso Kowacs
We extend the directional Poincaré inequality on the torus, introduced by Steinerberger in [Ark. Mat. 54 (2016), pp. 555--569], to the setting of compact Lie groups. We provide nec…
math.AP2024
Diagonal systems of differential operators on compact Lie groups
Paulo L. Dattori da Silva, Alexandre Kirilov, Ricardo Paleari da Silva
We investigate the global hypoellipticity and global solvability of systems of left-invariant differential operators on compact Lie groups. Focusing on diagonal systems, we establi…