Control of radii of convergence and extension of subanalytic functions

Details Control of radii of convergence and extension of subanalytic functions Control of radii of convergence and extension of subanalytic functions

2001-11-23

arxiv.org/abs/math/0111249v1

Mathematics

Complex Variables

AMS-TEX, 9 pages

Scientific paper

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)\S 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.

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