Method of re-quantization and its application to the construction of asymptotics for solutions of non-Fuchsian-type equations with holomorphic coefficients

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.