A Carleman type theorem for proper holomorphic embeddings

Gregery T. Buzzard; Franc Forstneric

doi:10.1007/BF02559596

A Carleman type theorem for proper holomorphic embeddings

复变函数 2016-09-06 v1

作者: Gregery T. Buzzard , Franc Forstneric

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摘要

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 $\C^n$ .

引用

@article{arxiv.math/9604221,
  title  = {A Carleman type theorem for proper holomorphic embeddings},
  author = {Gregery T. Buzzard and Franc Forstneric},
  journal= {arXiv preprint arXiv:math/9604221},
  year   = {2016}
}

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