A Carleman type theorem for proper holomorphic embeddings

Details A Carleman type theorem for proper holomorphic embeddings A Carleman type theorem for proper holomorphic embeddings

1996-04-04

arxiv.org/abs/math/9604221v1

Mathematics

Complex Variables

Scientific paper

10.1007/BF02559596

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 $\cC^r$ embedding of the real line into $\C^n$ can be approximated in the strong $\cC^r$ topology by a proper holomorphic embedding of $\C$ into $\C^n$.

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