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math.AP2026
Global hypoellipticity for perturbations of complex vector fields on the torus
Maria V. Bartmeyer, Paulo L. Dattori da Silva, Rafael B. Gonzalez
We apply Krönecker's approximation theorem to measure (in a topological sense) a set of constants which turn a vector field into a non-globally hypoelliptic operator. We present s…
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 ne…
math.AP2025
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…