On an integral representation of resurgent functions
type: Item
instance of: scholarly article
title: On an integral representation of resurgent functions
zbMATH Open document ID: 1065.30023
DOI: 10.1023/A:1012530014366
author: Boris Sternin
author: Victor Shatalov
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 30D15
Mathematics Subject Classification ID: 30E15
Mathematics Subject Classification ID: 34M37
Mathematics Subject Classification ID: 34Exx
Mathematics Subject Classification ID: 34M30
zbMATH DE Number: 1915934
zbMATH Keywords: asymptotic expansion
zbMATH Keywords: Borel-Laplace transform
zbMATH Keywords: resurgent solutions
zbMATH Keywords: simple singularities
reviewed by: Stancho Dimiev
MaRDI profile type: Publication
full work available at URL: a:1012530014366
OpenAlex ID: W162689400
description: scientific article; zbMATH DE number 1915934