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arXiv · 1212.4477

Nonlinear analysis with resurgent functions

David Sauzin
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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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David Sauzin. 2012-12-18. Nonlinear analysis with resurgent functions. https://arxiv.org/abs/1212.4477

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