Global hypoellipticity and global solvability for a class of operators on compact manifolds

摘要

We consider operators such as pseudo-differential operators on a manifold M-1. Let M-2 be another manifold, and consider P also as an operator on M-1 x M-2. We prove that, when P is injective in D' and symmetric, the following four properties of P are equivalent: global hypoellipticity on M-1 x M-2, global solvability on M-1 x M-2, global hypoellipticity on M-1, and global sovability on M-1. We apply this for a specific class of pseudo-differential operators on S-1 x M-2. (C) 1997 Academic Press.