In this work we present a new representation formula for ultradistributions using the so‐called ultradifferential operators. The main difference between our representation result and other works is that here we do not break the duality of Gevrey functions of other s and their ultradistributions, i.e., we locally represent an element of Ds′ by an infinite order operator acting on a function of class Gs. Our main application was in the local solvability of the differential complex associated to a locally integrable structure in a Gevrey environment.

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On T × G T \times G , where T T is a compact real-analytic manifold and G G is a compact Lie group, we consider differential operators P P which are invariant by left translations on G G and are elliptic in T T . Under a mild technical condition, we prove that global hypoellipticity of P P implies its global analytic-hypoellipticity (actually Gevrey of any order s ≥ 1 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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