English

Shatalov-Sternin's construction of complex WKB solutions and the associated Riemann surface

Classical Analysis and ODEs 2011-11-04 v4

Abstract

We re-examine Shatalov-Sternin's proof of existence of resurgent solutions of a linear ODE. In particular, we take a closer look at the "Riemann surface" (actually, a two-dimensional complex manifold) whose existence, endless continuability and other properties are claimed by those authors. We present a detailed argument for a part of the "Riemann surface" most relevant for the exact WKB method.

Keywords

Cite

@article{arxiv.0907.2934,
  title  = {Shatalov-Sternin's construction of complex WKB solutions and the associated Riemann surface},
  author = {Alexander Getmanenko},
  journal= {arXiv preprint arXiv:0907.2934},
  year   = {2011}
}

Comments

exposition improved, typos corrected