Osgood-Hartogs-type properties of power series and smooth functions


Journal Article

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 C∞ function f is proved when the restriction of f 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 can be regarded as problems of Osgood- Hartogs type. © 2011 by Pacific Journal of Mathematics.

Full Text

Cited Authors

  • Fridman, BL; Ma, D

Published Date

  • May 30, 2011

Published In

Volume / Issue

  • 251 / 1

Start / End Page

  • 67 - 79

International Standard Serial Number (ISSN)

  • 0030-8730

Digital Object Identifier (DOI)

  • 10.2140/pjm.2011.251.67

Citation Source

  • Scopus