Global solvability of real analytic involutive systems on compact manifolds. Part 2

Abstract

This work continues a previous study by Hounie and Zugliani on the global solvability of a locally integrable structure of tube type and a corank one, considering a linear partial differential operator L \mathbb L associated with a real analytic closed 1 1 -form defined on a real analytic closed n n -manifold. We deal now with a general complex form and complete the characterization of the global solvability of L . \mathbb L. In particular, we state a general theorem, encompassing the main result of Hounie and Zugliani. As in Hounie and Zugliani’s work, we are also able to characterize the global hypoellipticity of L \mathbb L and the global solvability of L n − 1 \mathbb L^{n-1} —the last nontrivial operator of the complex when M M is orientable—which were previously considered by Bergamasco, Cordaro, Malagutti, and Petronilho in two separate papers, under an additional regularity assumption on the set of the characteristic points of L . \mathbb L.

Globally hypoelliptic triangularizable systems of periodic pseudo‐differential operators

“…Investigations on pseudo-differential classes are also considered in the literature, for instance, [10,[13][14][15]28]. These problems are also analyzed in the setting of compact manifolds and Lie groups, for example, [1,2,9,22,25]. In particular, we point out that an important tool, present in all these references and here, is a Fourier analysis characterizing the functional spaces under investigation.…”