Fernando Sanz:

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 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. They may arise from natural problems such as differential or functional equations. We discuss several of their properties related to the ones from the standard analytic functions (such as o-mnimality) and prove a local monomialization result for generalized analytic functions: they can be transformed into a monomial via a locally finite collection of finite sequences of local blow-ups. (Joint work with J. P. Rolin and R. Martín).

Congreso: FOLGAm: Folheações e Geometria Algébrica em Minas.

Belo Horizonte (Brasil), 30 de Julio al 1 de Agosto de 2012.