Control of radii of convergence and extension of subanalytic functions

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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.
AMS-TEX, 9 pages

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Complex Variables, Commutative Algebra, Algebraic Geometry, 13J07, 14P10, 32B20

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http://salesiana.dossiersoluciones.com/handle/123456789/62714

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0111249
 http://arxiv.org/abs/math/0111249

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arXiv