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Shatalov‐Sternin's construction of complex WKB solutions and the choice of integration paths
Author(s) -
Getmanenko Alexander
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201100312
Subject(s) - wkb approximation , mathematics , ode , argument (complex analysis) , riemann surface , riemann hypothesis , pure mathematics , surface (topology) , manifold (fluid mechanics) , mathematical analysis , calculus (dental) , geometry , physics , quantum mechanics , mechanical engineering , medicine , biochemistry , chemistry , dentistry , engineering
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” relevant for the exact WKB method.