Control of Radii of Convergence and Extension of Subanalytic Functions

@inproceedings{Bierstone2001ControlOR,
  title={Control of Radii of Convergence and Extension of Subanalytic Functions},
  author={Edward Bierstone},
  year={2001}
}
Let g: U → R denote a real analytic function on an open subset U of Rn, and let Σ ⊂ ∂U denote the points where g does not admit a local analytic extension. We show that if g is semialgebraic (respectively, globally subanalytic), then Σ is semialgebraic (respectively, subanalytic) and g extends to a neighbourhood of U\Σ as an analytic function that is semialgebraic (respectively, globally subanalytic). (In the general subanalytic case, Σ is not necessarily subanalytic.) Our proof depends on… CONTINUE READING