Global hypoellipticity and global solvability in Gevrey classes on the n-dimensional torus

Abstract

Let P be a linear partial differential operator with coefficients in the Gevrey class G s ( T n ) where T n is the n-dimensional torus and s⩾1. We prove that if P is s-globally hypoelliptic in T n then its transposed operator tP is s-globally solvable in T n , thus extending to the Gevrey classes the well-known analogous result in the corresponding C ∞ class.