Abstract
Generalized power series extend the notion of formal power series by considering exponents of each variable ranging in a well 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.
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Martín Villaverde, R., Rolin, JP. & Sanz Sánchez, F. Local monomialization of generalized analytic functions. RACSAM 107, 189–211 (2013). https://doi.org/10.1007/s13398-012-0093-3
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DOI: https://doi.org/10.1007/s13398-012-0093-3