- 18-26 Alberto Lastra, Stephane Malek
- On parametric Borel summability for linear singularly perturbed
Cauchy problems with linear fractional transforms
Feb 27, 18
(auto. generated pdf),
of related papers
Abstract. We consider a family of linear singularly perturbed Cauchy problems which combines partial differential operators and linear
fractional transforms. We construct a collection of
holomorphic solutions on a full covering by sectors of a neighborhood of the origin in the complex plane with respect to
the perturbation parameter. This set is built up through classical and special Laplace transforms along
piecewise linear paths of functions which possess exponential or super exponential growth/decay on horizontal strips.
A fine structure which entails two levels of Gevrey asymptotics of order one and so-called order one plus is witnessed. Furthermore,
unicity properties regarding the one plus asymptotic layer are observed and follow from results on summability w.r.t a particular
strongly regular sequence recently obtained in a joint work with J. Sanz.