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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
34/2009

Shatalov-Sternin's construction of complex WKB solutions -- a comment on geometric issues.

Alexander Getmanenko

Abstract

We study Shatalov-Sternin's proof of existence of resurgent solutions of a linear ODE and discuss the construction of analytic continuation to a common ``Riemann surface'' of all terms of the von Neumann series appearing in their proof. We give a detailed proof of a more modest statement in a special situation.

Received:
Jul 17, 2009
Published:
Jul 17, 2009
MSC Codes:
34M37
Keywords:
WKB, resurgence

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Preprint
2009 Repository Open Access
Alexander Getmanenko

Shatalov-Sternin's construction of complex WKB solutions : a comment on geometric issues