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2024-06-21T10:10:56Z urn:hdl:10324/68176 Local monomialization of generalized analytic functions Martín Villaverde, Rafael Rolin, Jean-Philippe Sanz Sánchez, Fernando 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. 2024-06-21T10:10:56Z 2024-06-21T10:10:56Z 2012 info:eu-repo/semantics/article RACSAM (2013) 107:189–211 1578-7303 https://uvadoc.uva.es/handle/10324/68176 10.1007/s13398-012-0093-3 189 1 211 Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 107 1579-1505 eng info:eu-repo/semantics/openAccess Springer