Local monomialization of generalized real analytic functions

Abstract : Generalized power series extend the notion of formal power series by considering exponents ofeach variable ranging in a well ordered set of positive real numbers. Generalized analytic functionsare defined locally by the sum of convergent generalized power series with real coe cients. Weprove a local monomialization result for these functions: they can be transformed into a monomialvia a locally finite collection of finite sequences of local blowingsup. For a convenient frameworkwhere this result can be established, we introduce the notion of generalized analytic manifoldand the correct definition of blowing-up in this category.
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Rafael Martín Villaverde. Local monomialization of generalized real analytic functions. General Mathematics [math.GM]. Université de Bourgogne, 2011. English. ⟨NNT : 2011DIJOS108⟩. ⟨tel-01150953⟩

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