Abstract

This paper studies the asymptotic behavior with respect to the complex parameter of the fundamental solution for a second-order elliptic operator with smooth compact coefficients obtained by the V. P. Maslov canonical operator method using the results of V. V. Kucherenko.

It is shown that the singular part of the asymptotics can be represented as a series in Hankel functions of the first kind. The asymptotics are constructed under the assumption that all trajectories of the corresponding Hamiltonian system go to infinity.

中文翻译：

---

非均匀介质中的点源问题

摘要

本文利用VV Kucherenko 的结果，研究了通过VP Maslov 正则算子方法获得的具有光滑紧致系数的二阶椭圆算子基本解的复参数的渐近行为。

结果表明，渐近函数的奇异部分可以表示为第一类 Hankel 函数的级数。渐进是在相应哈密顿系统的所有轨迹趋于无穷大的假设下构建的。