Vol. 251, No. 1, 2011

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ISSN: 0030-8730
Osgood–Hartogs-type properties of power series and smooth functions

Buma L. Fridman and Daowei Ma

Vol. 251 (2011), No. 1, 67–79
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 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.

Keywords
formal power series, analytic functions, capacity
Mathematical Subject Classification 2000
Primary: 26E05, 30C85, 40A05
Milestones
Received: 5 May 2010
Revised: 24 August 2010
Accepted: 14 December 2010
Published: 22 April 2011

Proposed: Paul Yang
Authors
Buma L. Fridman
Department of Mathematics
Wichita State University
Wichita, KS 67260-0033
United States
Daowei Ma
Department of Mathematics
Wichita State University
Wichita, KS 67260-0033
United States