Posted January 21, 20202:30 pm - 3:20 pm Lockett 235
Sergio Carrillo, Universidad Sergio Arboleda, Bogata, Columbia
Gevrey power series solutions in analytic functions of first order holomorphic PDEs
Abstract: The goal of this talk is to explain a new Gevrey type -in an analytic function P- for formal power series solutions of some families of singular first order holomorphic PDEs. We will show that under a suitable geometric condition, if P generates the singular locus of the equation, then P is the generic source of divergence of the formal solution. In fact, our result recovers sistematically many well-known cases of singularly perturbed holomorhpic ODEs. The key estimates we use are based on Nagumo norms and their compatibilty with a Weierstrass division theorem. This work is a first step into the study of a Borel-type summability for these series as we shall describe by examples for the case P equal to a monomial.