18-26 Alberto Lastra, Stephane Malek

On parametric Borel summability for linear singularly perturbed Cauchy problems with linear fractional transforms (888K, pdf) Feb 27, 18

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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.

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