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 function is proved when the restriction of 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}
}
Comments
13 pages