Global analytic hypoellipticity of a class of degenerate elliptic operators on the torus (Q1902183)

The authors prove global analytic hypoellipticity on the torus for certain classes of operators, which have the form of a sum of squares of vector fields with real analytic coefficients. These classes contain some degenerate elliptic operators studied by Baouendi and Goulaouic. Under appropriate restrictions for the coefficients of operators, global analytic hypoellipticity is proved. It is shown that some operators, which are not locally analytic hypoelliptic, are globally analytic hypoelliptic.