Analyticity of Smooth CR Mappings of Generic Submanifolds

Abstract

We consider a smooth CR mapping f from a real-analytic generic subman- ifold M in C N into C N. For M of finite type and essentially finite at a point p ∈ M, and f formally finite at p, we give a necessary and sufficient condition forf to extend as a holomorphic mapping in some neighborhood of p. In a similar vein, we consider a formal holomorphic mapping H and give a necessary and sufficient condition forH to be convergent.