Asymptotic expansions and summability with respect to an analytic germ

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Asymptotic expansions and summability with respect to an analytic germ
Mozo Fernandez, Jorge (Universidad de Valladolid. Departamento de Algebra, Análisis Matemático, Geometría y Topología)
Schäfke, Reinhard (Université de Strasbourg. Institut de Recherche Mathématique Avancée)

Fecha:	2019
Resumen:	In a previous article [CMS], monomial asymptotic expansions, Gevrey asymptotic expansions, and monomial summability were introduced and applied to certain systems of singularly perturbed differential equations. In the present work, we extend this concept, introducing (Gevrey) asymptotic expansions and summability with respect to a germ of an analytic function in several variables - this includes polynomials. The reduction theory of singularities of curves and monomialization of germs of analytic functions are crucial to establish properties of the new notions, for example a generalization of the Ramis-Sibuya theorem for the existence of Gevrey asymptotic expansions. Two examples of singular differential equations are presented for which the formal solutions are shown to be summable with respect to a polynomial: one ordinary and one partial differential equation.
Ayudas:	Ministerio de Ciencia e Innovación MTM2010-15471
Nota:	Altres ajuts: ANR-10-BLAN 0102
Nota:	Altres ajuts: ANR-11-BS01-0009
Nota:	The first author was partially supported by the Spanish national project MTM2010-15471. The second author was supported in part by grants of the French National Research Agency (ref. ANR-10-BLAN 0102 and ANR-11-BS01-0009).
Derechos:	Tots els drets reservats.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió publicada
Materia:	Asymptotic expansions ; Summability
Publicado en:	Publicacions matemàtiques, Vol. 63 Núm. 1 (2019) , p. 3-79 (Articles) , ISSN 2014-4350

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