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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.
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Contributor : David Sauzin <>
Submitted on : Sunday, April 20, 2014 - 12:11:24 PM
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  • HAL Id : hal-00766749, version 4
  • ARXIV : 1212.4477



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⟩



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