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Extending analyticK-subanalytic functions

Artur Piękosz (2004)

Open Mathematics

Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.

Extending Tamm's theorem

Lou van den Dries, Chris Miller (1994)

Annales de l'institut Fourier

We extend a result of M. Tamm as follows:Let f : A , A m + n , be definable in the ordered field of real numbers augmented by all real analytic functions on compact boxes and all power functions x x r : ( 0 , ) , r . Then there exists N such that for all ( a , b ) A , if y f ( a , y ) is C N in a neighborhood of b , then y f ( a , y ) is real analytic in a neighborhood of b .

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