English

Osgood-Hartogs type properties of power series and smooth functions

Complex Variables 2011-01-21 v4

Abstract

We study the convergence of a formal power series of two variables if its restrictions on curves belonging to a certain family are convergent. Also analyticity of a given CC^\infty function ff is proved when the restriction of ff on analytic curves belonging to some family is analytic. Our results generalize two known statements: a theorem of P. Lelong and the Bochnak-Siciak Theorem. The questions we study fall into the category of "Osgood-Hartogs-type" problems.

Keywords

Cite

@article{arxiv.1005.0859,
  title  = {Osgood-Hartogs type properties of power series and smooth functions},
  author = {Buma L. Fridman and Daowei Ma},
  journal= {arXiv preprint arXiv:1005.0859},
  year   = {2011}
}

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13 pages