Local monomialization of generalized analytic functions

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 lo...

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Detalles Bibliográficos
Autores: Martín Villaverde, Rafael, Rolin, Jean-Philippe, Sanz Sánchez, Fernando
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2012
País:España
Institución:Universidad de Valladolid
Repositorio:UVaDOC. Repositorio Documental de la Universidad de Valladolid
OAI Identifier:oai:uvadoc.uva.es:10324/68176
Acceso en línea:https://doi.org/10.1007/s13398-012-0093-3
https://uvadoc.uva.es/handle/10324/68176
Access Level:acceso abierto
Palabra clave:Generalized power series · Blowing-up · Local monomialization
Descripción
Sumario: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.