On an integral representation of resurgent functions
In this paper a detailed exposition of the asymptotic approach to the resurgent function theory is given. Asymptotic expansions for analytic functions of exponential growth are studied via a complex analytic analogous of the Laplace transform, called Borel-Laplace transform. Interesting examples and counterexamples are given. Motivated by some special effects (``the possibility of different growth exponents in different directions'') the authors sketch a generalization of the theory of Borel-Laplace transform for functions of several variables. As an application resurgent solutions with simple singularities for ordinary differential equations are developed.
scientific article; zbMATH DE number 1915934