Artículo en colaboración R. Martín, J.-P. Rolin, F. Sanz, titulado:

"Local Monomialization of Generalized Analytic Functions" (23 pag.)

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas: Volume 107, Issue 1 (2013), Page 189-211


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.