(Semi-)Global Analytic Hypoellipticity for a class of "sums of squares" which fail to be locally analytic hypoelliptic

Abstract

The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced in "Analytic Hypoellipticity for Sums of Squares and the Treves Conjecture" by P. Albano and A. Bove and M. Mughetti, and in "Analytic Hypoellipticity for Sums of Squares and the Treves Conjecture. II" by A. Bove and M. Mughetti, satisfying the H\"ormander condition and which fail to be neither locally nor microlocally analytic hypoelliptic.