Global analytic hypoellipticity and solvability of certain operators subject to group actions

Araújo, Gabriel; Ferra, Igor; Ragognette, Luis

doi:10.1090/proc/16118

Global analytic hypoellipticity and solvability of certain operators subject to group actions
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by Gabriel Araújo, Igor A. Ferra and Luis F. Ragognette PDF

Proc. Amer. Math. Soc. 150 (2022), 4771-4783 Request permission

Abstract:

On $T \times G$, where $T$ is a compact real-analytic manifold and $G$ is a compact Lie group, we consider differential operators $P$ which are invariant by left translations on $G$ and are elliptic in $T$. Under a mild technical condition, we prove that global hypoellipticity of $P$ implies its global analytic-hypoellipticity (actually Gevrey of any order $s \geq 1$). We also study the connection between the latter property and the notion of global analytic (resp. Gevrey) solvability, but in a much more general setup.

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