Open Access
2019 Asymptotic expansions and summability with respect to an analytic germ
Jorge Mozo Fernández, Reinhard Schäfke
Publ. Mat. 63(1): 3-79 (2019). DOI: 10.5565/PUBLMAT6311901


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.


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Jorge Mozo Fernández. Reinhard Schäfke. "Asymptotic expansions and summability with respect to an analytic germ." Publ. Mat. 63 (1) 3 - 79, 2019.


Received: 2 February 2017; Revised: 27 November 2017; Published: 2019
First available in Project Euclid: 7 December 2018

zbMATH: 07040961
MathSciNet: MR3908786
Digital Object Identifier: 10.5565/PUBLMAT6311901

Primary: 41A60

Keywords: asymptotic expansions , summability

Rights: Copyright © 2019 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.63 • No. 1 • 2019
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