# Nonlinear analysis with resurgent functions

Abstract : We provide estimates for the convolution product of an arbitrary number of ''resurgent functions'', that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed discrete subset of $C$ which is stable under addition. Such estimates are then used to perform nonlinear operations like substitution in a convergent series, composition or functional inversion with resurgent functions, and to justify the rules of ''alien calculus''; they also yield implicitly defined resurgent functions. The same nonlinear operations can be performed in the framework of Borel-Laplace summability.
Mots-clés :
Document type :
Journal articles

Cited literature [34 references]

https://hal.archives-ouvertes.fr/hal-00766749
Contributor : David Sauzin <>
Submitted on : Sunday, April 20, 2014 - 12:11:24 PM
Last modification on : Thursday, April 29, 2021 - 12:06:08 PM
Long-term archiving on: : Monday, April 10, 2017 - 3:42:17 PM

### Files

NL_resur_CORREC_D_SAUZIN.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00766749, version 4
• ARXIV : 1212.4477

### Citation

David Sauzin. Nonlinear analysis with resurgent functions. Annales Scientifiques de l'École Normale Supérieure, Société mathématique de France, 2015, 48 (3), pp.667--702. ⟨hal-00766749v4⟩

Record views