MR2730623 Takahiro KAWAI, Tatsuya KOIKE and Yoshitsugu TAKEI Takahiro KAWAI, Tatsuya KOIKE and Yoshitsugu TAKEI On the Structure of Higher Order Simple-Pole Type Operators in Exact WKB Analysis Funkcialaj Ekvacioj. Serio Internacia 53 2010 249--276 http://fe.math.kobe-u.ac.jp/FE/FullPapers/53-2/53_249.pdf http://www.ams.org/mathscinet-getitem?mr=MR2730623 We introduce an appropriate class of higher order linear ordinary differential operators with a large parameter and with simple poles in their coefficients, and study their structure from the viewpoint of exact WKB analysis, i.e., the WKB analysis based on the Borel resummation. Our main result is that an operator in the class is expressed as a product of two operators $Q$ and $R$, with $Q$ being irrelevant to the Stokes geometry and with $R$ being a second order simple-pole type operator studied by Koike ([12], [13], [14]). This decomposition theorem gives us a connection formula for WKB solutions near the simple pole in question, and it is used to explain the background mechanism of some intriguing phenomenon we encounter in the study of a particular third order operator. Some discussions on the scope of the future development of the theory are included. Exact WKB analysis, Simple pole-type operators. 34M60; 34M40. 53-249 2010 On the Structure of Higher Order Simple-Pole Type Operators in Exact WKB Analysis Takahiro KAWAI, Tatsuya KOIKE and Yoshitsugu TAKEI Takahiro KAWAI, Tatsuya KOIKE and Yoshitsugu TAKEI
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