Geodesic
Method of re-quantization and its application to the construction of asymptotics for solutions of non-Fuchsian-type equations with holomorphic coefficients
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 72-85

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In this paper, we apply methods of resurgent analysis (including the method of repeated quantization) 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 method of repeated quantization, we construct asymptotics for solutions of an ordinary differential equation with holomorphic coefficients in a neighborhood of infinity.
Keywords: Fuchsian linear differential equation, irregular singular point, asymptotics, resurgent function, principal symbol of a differential operator
Mots-clés : Laplace–Borel transform, method of re-quantization. 
@article{INTO_2019_173_a6,
     author = {M. V. Korovina and V. Yu. Smirnov},
     title = {Method of re-quantization and its application to the construction of asymptotics for solutions of {non-Fuchsian-type} equations with holomorphic coefficients},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {72--85},
     publisher = {mathdoc},
     volume = {173},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_173_a6/}
}
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M. V. Korovina; V. Yu. Smirnov. Method of re-quantization and its application to the construction of asymptotics for solutions of non-Fuchsian-type equations with holomorphic coefficients. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 4, Tome 173 (2019), pp. 72-85. http://geodesic.mathdoc.fr/item/INTO_2019_173_a6/