Local monomialization of generalized analytic functions

Abstract

Generalized power series extend the notion of formal power series by considering exponents of each variable ranging in awell ordered set of positive real numbers.Generalized analytic functions are defined locally by the sum of convergent generalized power series with real coefficients. We prove a local monomialization result for these functions: they can be transformed into a monomial via a locally finite collection of finite sequences of local blowings-up. For a convenient framework where this result can be established, we introduce the notion of generalized analytic manifold and the correct definition of blowing-up in this category.