Sauzin, David Nonlinear analysis with resurgent functions. (Analyse non linéaire pour les fonctions résurgentes.) (English. French summary) Zbl 1326.30036 Ann. Sci. Éc. Norm. Supér. (4) 48, No. 3, 667-702 (2015). Summary: We provide estimates for the convolution product of an arbitrary number of “resurgent functions”, that is holomorphic germs at the origin of \(\mathbb C\) that admit analytic continuation outside a closed discrete subset of \(\mathbb C\) 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. Cited in 5 Documents MSC: 30E99 Miscellaneous topics of analysis in the complex plane 30B40 Analytic continuation of functions of one complex variable Keywords:holomorphic germs, analytic continuation; convolution product; Borel summability PDFBibTeX XMLCite \textit{D. Sauzin}, Ann. Sci. Éc. Norm. Supér. (4) 48, No. 3, 667--702 (2015; Zbl 1326.30036) Full Text: DOI arXiv Link