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Global hypoellipticity and global solvability in Gevrey classes on the n-dimensional torus |
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| Authors: | AA Albanese L Zanghirati |
| Institution: | a Dipartimento di Matematica “E. De Giorgi”, Università degli Studi di Lecce, Via Per Arnesano, P.O. Box 193, I-73100 Lecce, Italy b Dipartimento di Matematica, Università degli Studi di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy |
| Abstract: | Let P be a linear partial differential operator with coefficients in the Gevrey class Gs(Tn) where Tn is the n-dimensional torus and s?1. We prove that if P is s-globally hypoelliptic in Tn then its transposed operator tP is s-globally solvable in Tn, thus extending to the Gevrey classes the well-known analogous result in the corresponding C∞ class. |
| Keywords: | s-Globally hypoelliptic s-Globally solvable Gevrey spaces of order s |
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