Analytic Hypoellipticity in the Presence of Lower Order Terms

Albano, Paolo; Bove, Antonio; Tartakoff, David S.

Analytic Hypoellipticity in the Presence of Lower Order Terms

Authors

Albano, Paolo

Bove, Antonio

Tartakoff, David S.

Description

We consider a second order operator with analytic coefficients whose principal symbol vanishes exactly to order two on a symplectic real analytic manifold. We assume that the first (non degenerate) eigenvalue vanishes on a symplectic submanifold of the characteristic manifold. In the $C^\infty$ framework this situation would mean a loss of 3/2 derivatives. We prove that this operator is analytic hypoelliptic. The main tool is the FBI transform. A case in which $C^\infty$ hypoellipticity fails is also discussed.
40 pages