22/07/2016, 10:00 — 11:00 — Anfiteatro Ea1, Torre Norte (Electricidade)
David Sauzin, CNRS Paris & SNS Pisa

Nonlinear Analysis with Endlessly Continuable Functions

A holomorphic germ at 0 is said to be endlessly continuable if it enjoys a certain property of analytic continuation which guarantees that the possible singularities are locally isolated; the singular locus is not fixed in advance and, in projection on the complex plane, it can have accumulation points. It is natural to call resurgent the formal series whose Borel transforms enjoy this property. We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power series. In particular, this proves that the exponential or the logarithm of a resurgent series is resurgent.

[Joint work with Shingo Kamimoto]