Abstract
In this paper, we apply methods of resurgent analysis (including the requantization method) to the construction of asymptotics for solutions of linear ordinary differential equations with holomorphic coefficients. We provide a classification of various types of asymptotics depending on the principal symbol of the differential operator. Using the requantization method, we construct asymptotics for solutions of an ordinary differential equation with holomorphic coefficients in a neighborhood of infinity.
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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 172, Proceedings of the Voronezh Winter Mathematical School “Modern Methods of Function Theory and Related Problems,” Voronezh, January 28 – February 2, 2019. Part 3, 2019.
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Korovina, M.V., Smirnov, V.Y. Requantization Method and Its Application to the Construction of Asymptotics for Solutions of Non-Fuchsian Equations with Holomorphic Coefficients. J Math Sci 268, 70–83 (2022). https://doi.org/10.1007/s10958-022-06181-4
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DOI: https://doi.org/10.1007/s10958-022-06181-4
Keywords and phrases
- Fuchsian linear differential equation
- irregular singular point
- asymptotics
- resurgent function
- Laplace–Borel transform
- principal symbol of a differential operator
- requantization method