On the global solvability in Gevrey classes on the n-dimensional torus

Let P be a linear partial differential operator with coefficients in the Gevrey class Gs(T n), where T n is the n-dimensional torus and s 1. We prove a necessary condition for the s-global solvability of P on T n. We also apply this result to give a complete characterization for the s-global solvability for a class of formally self-adjoint operators with nonconstant coefficients.  2004 Elsevier Inc. All rights reserved