Analyticity of Smooth CR Mappings of Generic Submanifolds

Abstract

We consider a smooth CR mapping $f$ from a real-analytic generic submanifold $M$ in $\Bbb C^N$ into $\Bbb C^N$. For $M$ of finite type and essentially finite at a point $p\in\ M$, and $f$ formally finite at $p$, we give a necessary and sufficient condition for $f$ 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 for $H$ to be convergent.