Global hypoellipticity and global solvability for a class of operators on compact manifolds
Let \(M_1, M_2\) be smooth compact oriented manifolds and let \(P: C^\infty (M_1) \to C^\infty (M_1)\) be a continuous linear operator, admitting continuous extension \({}^t P: D'(M_1) \to D'(M_1)\). The authors prove that if \(P\) and \(^t P\) are injective, then the following properties are equivalent: (i) \(P\) and \(^t P\) are globally hypoelliptic on \(M_1\times M_2\); (ii) \(P\) and \({}^tP\) are globally solvable on \(M_1\times M_2\); (iii) \(P\) and \({}^tP\) are globally hypoelliptic on \(M_1\); (iv) \(P\) and \({}^tP\) are globally solvable on \(M_1\).
scientific article; zbMATH DE number 1109511