A CARLEMAN TYPE THEOREM FOR PROPER HOLOMORPHIC EMBEDDINGS

GREGERY T. BUZZARD FRANC FORSTNERIC

Abstract. In 1927, Carleman showed that a continuous, complex-valued function on the real line can be approximated in the Whitney topology by an entire function restricted to the real line. In this paper, we prove a similar result for proper holomorphic embeddings. Namely, we show that a proper C^{r} embedding of the real line into ℂ^{n} can be approximated in the strong C^{r} topology by a proper holomorphic embedding of ℂ into ℂ^{n}.