chapter  10
8 Pages

Global Hypoellipticity in the Schwartz Space

We give in this chapter two proofs of Theorem 10.1 on the global hypoellipticity in S of the perturbed Laplacian −∆+m2, where m is a positive constant. The first proof is elementary and the second proof is deeper in the sense that it probes the behavior of the Bessel potential at infinity. Both proofs depend on Lemma 10.3.