Hypoellipticity and existence of periodic solutions on \(T^ d\) (Q914051)

The author investigates global solvability and global hypoellipticity for partial differential equations and pseudo-differential equations on the n-torus \(T^ n\); in particular necessary and sufficient conditions are expressed in the frame of the Gevrey classes \(G^ s(T^ n)\), \(s\geq 1\), for operators of the form \[ P=p_ m(D)+p_{m-1}(x,D), \] where \(p_ m(\xi)\) is a polynomial of degree m, and \(p_{m-1}(x,\xi)\) is a classical pseudo-differential symbol of order m-1.