Nonlinear analysis with resurgent functions

David Sauzin (1)

1 Laboratoire Fibonacci

We provide estimates for the convolution product of an arbitrary number of resurgent functions, more precisely of $\Omega$-continuable germs, where $\Omega$ is a closed discrete subset of the complex plane which is stable under addition. Such estimates are needed 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.

Mots clés: Resurgent functions; convolution product

Domaines: Systèmes dynamiques [math.DS]

David Sauzin. Nonlinear analysis with resurgent functions. 2012. ⟨hal-00766749v3⟩