Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Control of radii of convergence and extension of subanalytic functions
HTML articles powered by AMS MathViewer

by Edward Bierstone PDF
Proc. Amer. Math. Soc. 132 (2004), 997-1003 Request permission


Let $g$: $U\to \mathbb {R}$ denote a real analytic function on an open subset $U$ of $\mathbb {R}^n$, and let $\Sigma \subset \partial U$ denote the points where $g$ does not admit a local analytic extension. We show that if $g$ is semialgebraic (respectively, globally subanalytic), then $\Sigma$ is semialgebraic (respectively, subanalytic) and $g$ extends to a semialgebraic (respectively, subanalytic) neighbourhood of $\overline {U}\backslash \Sigma$. (In the general subanalytic case, $\Sigma$ is not necessarily subanalytic.) Our proof depends on controlling the radii of convergence of power series $G$ centred at points $b$ in the image of an analytic mapping $\varphi$, in terms of the radii of convergence of $G\circ \widehat {\varphi }_a$ at points $a\in \varphi ^{-1}(b)$, where $\widehat {\varphi }_a$ denotes the Taylor expansion of $\varphi$ at $a$.
Similar Articles
Additional Information
  • Edward Bierstone
  • Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
  • Email:
  • Received by editor(s): December 16, 2002
  • Published electronically: September 5, 2003
  • Additional Notes: The author’s research was partially supported by NSERC grant 0GP0009070
  • Communicated by: Mei-Chi Shaw
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 997-1003
  • MSC (2000): Primary 13J07, 14P10, 32B20; Secondary 13J05, 32A10
  • DOI:
  • MathSciNet review: 2045414