Propagation of Holomorphic Extendability of CR Functions.
Let be a bounded, convex and open set with real analytic boundary. Let be the tube with base and let be the Bergman kernel of . If is strongly convex, then is analytic away from the boundary diagonal. In the weakly convex case this is no longer true. In this situation, we relate the off diagonal points where analyticity fails to the Trèves curves. These curves are symplectic invariants which are determined by the CR structure of the boundary of . Note that Trèves curves exist only...
Let be a linear partial differential operator with analytic coefficients. We assume that is of the form “sum of squares”, satisfying Hörmander’s bracket condition. Let be a characteristic point for . We assume that lies on a symplectic Poisson stratum of codimension two. General results of Okaji show that is analytic hypoelliptic at . Hence Okaji has established the validity of Treves’ conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of...
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