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On the exact WKB analysis of operators admitting infinitely many phases |
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| Authors: | Takashi Aoki Takahiro Kawai Tatsuya Koike Yoshitsugu Takei |
| Affiliation: | a Department of Mathematics and Physics, The School of Science and Engineering, Kinki University, Higashi-Osaka, 577-8502 Japan b Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502 Japan c Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606-8502 Japan |
| Abstract: | To analyze differential operators whose WKB solutions admit infinitely many phases, we introduce a class of differential operators of WKB type and analyze their exact WKB theoretic structure near their turning points. Our analysis makes full use of techniques and ideas in microlocal analysis; we use a quantized contact transformation to construct a WKB solution of a differential equation of WKB type, and we use a Späth-type division theorem for a differential operator of WKB type to study its structure near turning points. As an application, we show a connection formula for WKB solutions near a simple turning point. |
| Keywords: | Operator of WKB type Exact WKB analysis Infinitely many phases Turning point Stokes curve Connection formula |
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