On a Problem Arising in Application of the Re-Quantization Method to Construct Asymptotics of Solutions to Linear Differential Equations with Holomorphic Coefficients at Infinity

Abstract

The re-quantization method-one of the resurgent analysis methods of current importance-is developed in this study. It is widely used in the analytical theory of linear differential equations. With the help of the re-quantization method, the problem of constructing the asymptotics of the inverse Laplace-Borel transform is solved for a particular type of functions with holomorphic coefficients that exponentially grow at zero. Two examples of constructing the uniform asymptotics at infinity for the second-and forth-order differential equations with the help of the re-quantization method and the result obtained in this study are considered.

Asymptotics of Solutions of Linear Differential Equations with Holomorphic Coefficients in the Neighborhood of an Infinitely Distant Point

“…For this particular case, the asymptotics of the solution of the model equation are constructed in the neighborhood of an infinitely distant point by the re-quantization method. Despite the fact that in this study we consider a significantly more general case that comprises a broad class of equations, including the model equation of [18], some stages of the proof for this model problem coincide with those presented in [18]. Therefore, we make references to [18] at the points where the proofs are identical.…”

“…Despite the fact that in this study we consider a significantly more general case that comprises a broad class of equations, including the model equation of [18], some stages of the proof for this model problem coincide with those presented in [18]. Therefore, we make references to [18] at the points where the proofs are identical. It is possible to read about the model problem below.…”

“…Earlier, the re-quantization method was used in [18,19]. In [18] a particular case of Equation ( 1), i.e., a model problem, was considered.…”

“…Earlier, the re-quantization method was used in [18,19]. In [18] a particular case of Equation ( 1), i.e., a model problem, was considered. For this particular case, the asymptotics of the solution of the model equation are constructed in the neighborhood of an infinitely distant point by the re-quantization method.…”

Метод Повторного Квантования И Его Применение К Построению Асимптотик Решений Уравнений Нефуксова Типа С Голоморфными Коэффициентами

“…Теорема 2 (см. [17]). Асимптотика функции B −1 e −α/p k/n g(p) в окрестности нуля имеет вид Назовем асимптотики типа (24) обобщенными асимптотиками нефуксова типа.…”