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On the exact WKB analysis of operators admitting infinitely many phases. (English) Zbl 1056.34103
The paper is devoted to the analysis of differential operators whose WKB solutions admit infinitely many phases. Therefore, a suitable class of differential operators of WKB type is introduced and their exact WKB theoretic structure near their turning points is analysed. The main tools are techniques and ideas in microlocal analysis, a quantized contact transformation and a Späth-type division theorem. The results are applied to derive a connection formula for WKB solutions near a simple turning point.

34M60 Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent)
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
Full Text: DOI
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