2001/11/23 by Edward Bierstone, Bierstone, Edward
Mathematics · #13J07 #14P10 #32B20 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics #math.AC #math.AG #math.CV #msc:13J07 #msc:14P10 #msc:32B20
paper · pdf · doi:10.48550/arxiv.math/0111249
AMS-TEX, 9 pages
arxiv created 2001/11/23 · arxiv updated 2009/11/30
Let g denote a real analytic function on an open subset U of Euclidean space, and let S denote the boundary points of U where g does not admit a local analytic extension. We show that if g is semialgebraic (respectively, globally subanalytic), then S is semialgebraic (respectively, subanalytic) and g extends to a neighbourhood of cl(U)§as an analytic function that is semialgebraic (respectively, globally subanalytic). (In the general subanalytic case, S is not necessarily subanalytic.) Our proof depends on controlling the radii of convergence of power series G centred at points in the image of an analytic mapping, in terms of the radii of convergence of the pull-backs of G at points of the source.