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

Alexander Getmanenko
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Submission date: 17. Jul. 2009
Pages: 42
MSC-Numbers: 34M37
Keywords and phrases: WKB, resurgence
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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.